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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-Q

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                        MANAGEMENT INVESTMENT COMPANIES



		Investment Company Act file number 811-09223


                    Pioneer Municipal High Income Trust Fund;
               (Exact name of registrant as specified in charter)


                       60 State Street, Boston, MA 02109
              (Address of principal executive offices) (ZIP code)


            Dorothy E. Bourassa, Pioneer Investment Management, Inc.,
                       60 State Street, Boston, MA 02109
                    (Name and address of agent for service)


Registrant's telephone number, including area code:  (617) 742-7825


Date of fiscal year end:  October 31

Date of reporting period:  January 31, 2005

Form N-Q is to be used by management investment companies, other than small 
business investment companies registered on Form N-5 (239.24 and 274.5 of this
chapter), to file reports with the Commission, not later than 60 days after
close of the first and third fiscal quarters, pursuant to Rule 30b1-5under
the Investment Company Act of 1940 (17 CFR 270.30b-5).  The Commission may
use the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-Q
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 450 Fifth Street, NW,
Washington, DC 20549-0609.  The OMB has reviewed this collection of information
under the clearance requirements of 44 U.S.C. ss. 3507.



ITEM 1. Schedule of Investments.
                                   


                    Pioneer Municipal High Income Trust

                    SCHEDULE OF INVESTMENTS 1/31/05 (unaudited)

Principal  S&P/Moody's
Amount     Ratings                                                                                                    Value
                    TAX EXEMPT OBLIGATIONS  - 126.4% of Net Assets
                    Alabama - 3.5%
10000000   AAA/Aaa  Birmingham Alabama General Obligation, 5.0%, 12/1/32                                              10,386,600
1500000    BBB/NR   Camden Alabama Industrial Development Board, 6.125%, 12/1/24                                      1,625,325
                                                                                                                      12,011,925
                    Arizona - 7.1%
5000000    B+/Ba3   Apache County Industrial Development Authority, 5.85%, 3/1/28                                     4,999,600
5000000    B+/Ba3   Apache County Industrial Development Authority, 5.875%, 3/1/33                                    4,999,550
11630000   BB-/Ca   Gila County Industrial Development Authority, 5.55%, 1/1/27                                       9,745,475
3000000    NR/NR    Maricopa County Industrial Development Authority, 7.875%, 4/1/27                                  3,097,380
1000000    NR/Baa3  Pima County Industrial Development Authority, 7.25%, 7/1/31                                       1,069,250
500000     NR/Baa2  Yavapai County Industrial Development Authority, 6.0%, 8/1/33                                     531,790
                                                                                                                      24,443,045
                    California - 10.5%
7270000    A/A3     California State General Obligation, 5.25%, 2/1/28                                                7,710,126
5150000    BBB/Baa3 Golden State Tobacco Securitization Corp., 7.8%, 6/1/42                                           5,725,358
7000000    BBB/Baa3 Golden State Tobacco Securitization Corp., 7.875%, 6/1/42                                         7,815,990
4000000    AAA/Aaa  Palm Desert Financing Authority Tax Allocation Revenue, 5.0%, 4/1/30                              4,160,040
3000000    AAA/Aaa  San Diego Unified School District, 5.0%, 7/1/25                                                   3,165,630
2500000    AAA/Aaa  University of California Revenue, 5.0%, 5/15/25                                                   2,661,550
5000000    B+/NR    Valley Health System Hospital Revenue, 6.5%, 5/15/25                                              4,955,450
                                                                                                                      36,194,144
                    Connecticut - 3.3%
2205000    BB/Ba1   Connecticut State Health & Educational Facilities Authority Revenue, 5.375%, 7/1/17               2,123,702
4400000    BB/Ba1   Connecticut State Health & Educational Facilities Authority Revenue, 5.5%, 7/1/27                 4,044,304
5000000    BB+/NR   Mohegan Tribe Indians Gaming Authority, 6.25%, 1/1/31                                             5,309,200
                                                                                                                      11,477,206
                    District of Columbia - 3.6%
5000000    BBB/Baa3 District of Columbia Tobacco Settlement Financing Corp., 6.5%, 5/15/33                            5,012,250
7325000    BBB/Baa3 District of Columbia Tobacco Settlement Financing Corp., 6.75%, 5/15/40                           7,424,766
                                                                                                                      12,437,016
                    Florida - 4.3%
2000000    NR/NR    Beacon Lakes Community Development, 6.9%, 5/1/35                                                  2,104,360
2300000    CC/C     Hillsborough County Aviation Authority Revenue, 6.8%, 1/1/24                                      1,242,000
1650000    BBB-/Baa2Polk County Industrial Development Revenue, 5.85%, 12/1/30                                        1,691,943
2000000    NR/NR    Seminole Tribe Convention-A, 8.95%, 10/1/33                                                       2,263,380
1900000    NR/NR    Seminole Tribe Convention-A, 10.0%, 10/1/33                                                       2,159,635
5000000    NR/Baa2  Tallahassee Health Facilities Revenue, 6.375%, 12/1/30                                            5,210,550
                                                                                                                      14,671,868

                    Georgia - 0.4%
1325000    NR/NR    Brunswick & Glynn County Development Authority Revenue, 7.25%, 1/1/35                             1,325,715

                    Idaho - 1.5%
5000000    BB+/Ba3  Power County Industrial Development Corp., 6.45%, 8/1/32                                          5,137,500

                    Illinois - 4.2%
1000000    NR/NR    Centerpoint Intermodal Center, 8.0%, 6/15/23 (144A)                                               977,600
3810000    CC/C     Chicago Illinois O'Hare International Airport, 6.45%, 5/1/18                                      1,790,700
1500000    NR/NR    Illinois Health Facilities Authority Revenue, 6.9%, 11/15/33                                      1,517,865
16880000(a)AAA/Aaa  Metropolitan Pier & Exposition Authority Dedicated State Tax Revenue,
                       0.0%, 6/15/22                                                                                  10,243,459
                                                                                                                      14,529,624
                    Indiana - 1.6%
1000000    BBB+/Baa1Indiana State Development Finance Authority Revenue, 5.6%, 12/1/32                                1,031,160
4300000    BB+/Caa2 Indiana State Development Finance Authority Revenue, 5.75%, 10/1/11                               4,455,230
                                                                                                                      5,486,390
Principal  S&P/Moody's
Amount     Ratings                                                                                                    Value
                    Kentucky - 2.3%
7050000    CC/Ca    Kenton County Airport Revenue, 7.5%, 2/1/12                                                       6,242,281
1965000    CC/Ca    Kenton County Airport Revenue, 7.5%, 2/1/20                                                       1,654,137
                                                                                                                      7,896,418
                    Massachusetts - 9.2%
2435000    AAA/Aaa  Massachusetts Health & Educational Facilities Authority Revenue, 5.0%, 7/15/35                    2,523,196
7050000    AAA/Aaa  Massachusetts Health & Educational Facilities Authority Revenue, 5.125%, 7/15/37                  7,391,361
1000000    AA/NR    Massachusetts Health & Educational Facilities Authority Revenue, 5.25%, 10/15/33                  1,061,620
3500000    BBB/Baa3 Massachusetts Health & Educational Facilities Authority Revenue, 6.25%, 7/1/22                    3,756,445
5000000    BBB-/NR  Massachusetts Health & Educational Facilities Authority Revenue, 6.75%, 10/1/33                   5,337,000
75000      BB/NR    Massachusetts State Development Finance Agency, 5.25%, 10/1/18                                    69,140
5000000    AAA/Aaa  Massachusetts State Development Finance Agency, 5.75%, 1/1/42                                     6,141,050
5055000    AA-/Aa3  Massachusetts State Housing Finance Agency, 5.25%, 12/1/33                                        5,132,999
                                                                                                                      31,412,811
                    Michigan - 4.6%
1500000    BBB-/NR  John Tolfree Health System Corp., 6.0%, 9/15/23                                                   1,464,420
2000000    B/Ba3    Michigan State Hospital Finance Authority Revenue, 5.5%, 8/15/23                                  1,849,000
4010000    BBB-/Ba1 Michigan State Hospital Finance Authority Revenue, 6.0%, 2/1/24                                   3,903,775
2000000    NR/NR    Michigan State Hospital Finance Authority Revenue, 6.4%, 1/1/15                                   2,005,320
7690000    NR/NR    Wayne Charter County Michigan Special Airport Facilities Revenue, 6.75%, 12/1/15                  6,720,522
                                                                                                                      15,943,037
                    Minnesota - 4.5%
1675000    BB/NR    Duluth Economic Development Authority Health Care Facilities Revenue, 7.25%,  6/15/32             1,764,897
13260000   NR/NR    Minneapolis/St. Paul Metropolitan Airports, 7.0%, 4/1/25                                          12,302,495
1430000    BB+/Ba1  St. Paul Housing & Redevelopment Authority, 6.625%, 11/1/17                                       1,441,469
                                                                                                                      15,508,861
                    Mississippi - 0.9%
3000000    BBB/Ba1  Mississippi Business Finance Corp. Pollution Control Revenue, 5.9%, 5/1/22                        3,029,160

                    Missouri - 1.4%
5500000    NR/B3    St. Louis Industrial Development Authority Revenue, 7.25%, 12/15/35                               4,627,920

                    Nevada - 1.4%
1000000    BBB-/Baa2Clark County Industrial Development Revenue, 5.45%, 3/1/38                                        1,064,440
1850000    B-/NR    Clark County Industrial Development Revenue, 5.5%, 10/1/30                                        1,799,051
2000000    NR/NR    Nevada State Department of Business & Industry, 7.25%, 1/1/23                                     2,042,000
                                                                                                                      4,905,491
                    New Hampshire - 0.9%
3000000    AAA/Aaa  Manchester School Facilities Revenue, 5.125%, 6/1/28                                              3,181,110

                    New Jersey - 8.2%
2000000    B/Caa2   New Jersey Economic Development Authority Revenue, 6.25%, 9/15/19                                 1,671,020
11700000   B/Caa2   New Jersey Economic Development Authority Revenue, 6.25%, 9/15/29                                 9,308,169
1000000    B/Caa2   New Jersey Economic Development Authority Revenue, 6.4%, 9/15/23                                  829,520
6150000    B/Caa2   New Jersey Economic Development Authority Revenue, 7.0%, 11/15/30                                 5,327,130
10750000   BBB/Baa3 Tobacco Settlement Financing Corp., 6.75%, 6/1/39                                                 10,926,407
                                                                                                                      28,062,246
                    New Mexico - 1.6%
3700000  + NR/NR    New Mexico Hospital Equipment Loan Council, 6.4%, 6/1/16                                          3,947,974
1350000    BBB-/NR  Santa Fe Educational Facilities Revenue, 5.75%, 10/1/28                                           1,363,838
                                                                                                                      5,311,812
                    New York - 5.8%
2000000    A/NR     New York City Industrial Development Agency, 5.375%, 6/1/23                                       2,086,140
5625000    CCC/Caa2 New York City Industrial Development Agency, 6.9%, 8/1/24                                         4,216,950
5000000    AAA/Aaa  New York City Trust Cultural Resources Revenue, 5.125%, 7/1/31                                    5,249,700
2000000    NR/NR    Suffolk County Industrial Development Agency, 7.25%, 1/1/30                                       1,995,240
6000000    AAA/Aaa  Triborough Bridge & Tunnel Authority Revenue, 5.25%, 11/15/30                                     6,458,640
                                                                                                                      20,006,670
                    North Carolina - 0.6%
4600000 (b)NR/NR    Charlotte North Carolina Special Facilities Revenue, 7.75%, 2/1/28                                2,208,000

Principal  S&P/Moody's
Amount     Ratings                                                                                                    Value
                    Oklahoma - 5.0%
3000000  ++AAA/Aaa  Oklahoma Development Finance Authority Revenue, 5.625%, 8/15/19                                  3,350,550
8000000  ++AAA/Aaa  Oklahoma Development Finance Authority Revenue, 5.625%, 8/15/29                                  8,913,200
4100000    B-/Caa2  Tulsa Municipal Airport Revenue, 5.65%, 12/1/35                                                  3,882,085
1225000    B-/Caa2  Tulsa Municipal Airport Revenue, 6.25%, 6/1/20                                                   1,030,311
                                                                                                                     17,176,146
                    Oregon - 4.6%
1000000    NR/NR    Klamath Falls Electric Revenue, 5.75%, 1/1/13                                                    1,018,130
7000000    NR/NR    Klamath Falls Electric Revenue, 6.0%, 1/1/25                                                     7,053,200
7500000    NR/NR    Western Generation Agency Cogeneration Project Revenue, 7.125%, 1/1/21                           7,684,200
                                                                                                                     15,755,530
                    Pennsylvania - 7.1%
1550000    NR/Baa1  Allegheny County Hospital Development Authority Revenue, 5.125%, 5/1/25                          1,452,970
12300000   B/B1     Allegheny County Hospital Development Authority Revenue, 9.25%, 11/15/30                         14,285,343
1000000    BB-/NR   Columbia County Hospital Authority Health Care Revenue, 5.9%, 6/1/29                             868,230
1000000    BBB/Ba2  Hazleton Health Services Authority Hospital Revenue, 5.625%, 7/1/17                              924,550
1280000    NR/B2    Langhorne Manor Borough Higher Education & Health Authority Revenue, 7.35%, 7/1/22               1,273,178
500000     BBB+/NR  Pennsylvania Higher Educational Facilities Authority Revenue, 5.4%, 7/15/36                      520,850
5000000    BBB-/Baa3Philadelphia Hospitals & Higher Education Facilities Authority Revenue, 6.5%, 11/15/22           4,999,850
                                                                                                                     24,324,971
                    South Carolina - 8.0%
4250000    BBB/Baa2 Georgetown County Environmental Improvement Revenue, 5.95%, 3/15/14                              4,806,835
15000000   AA-/A1   Greenville County School District, 5.5%, 12/1/28                                                 16,147,650
5850000    BBB/Baa2 South Carolina Jobs Economic Development Authority Revenue, 6.375%, 8/1/34                       6,341,224
                                                                                                                     27,295,709
                    Tennessee  - 3.8%
7000000    BBB+/Baa2Johnson City Health & Educational Facilities Board Hospital Revenue, 7.5%, 7/1/33                8,332,100
4480000    NR/Baa3  Knox County Health Educational & Housing Facilities Board Hospital Revenue, 6.375%, 4/15/22      4,602,304
                                                                                                                     12,934,404
                    Texas  - 7.6%
7500000    CCC/Caa2 Alliance Airport Authority Special Facilities Revenue, 7.5%, 12/1/29                             5,437,800
1345000    NR/Baa3  Bexar County Housing Finance Corp., 8.0%, 12/1/36                                                1,404,409
2500000    BBB-/Ba2 Brazos River Authority Revenue, 5.375%, 4/01/19                                                  2,583,325
5000000    CCC/Caa2 Dallas-Fort Worth International Airport Revenue, 6.15%, 5/1/29                                   4,591,700
485000     CC/Ca    Dallas-Fort Worth International Airport Revenue, 6.25%, 11/1/13                                  227,950
7750000    CC/Ca    Dallas-Fort Worth International Airport Revenue, 7.125%, 11/1/26                                 3,410,000
4000000    NR/NR    Decatur Hospital Authority Revenue, 7.0%, 9/1/25                                                 4,228,320
1000000    BB/NR    Georgetown Health Facilities Development Corp., 6.25%, 8/15/29                                   1,014,190
3750000    B-/Caa2  Houston Airport System Special Facilities Revenue, 5.7%, 7/15/29                                 2,675,850
500000     BBB/Baa2 Sabine River Authority Pollution Control Revenue, 6.15%, 8/1/22                                  556,520
                                                                                                                     26,130,064
                    Vermont  - 0.5%
1500000    A-/A3    Vermont Educational & Health Buildings Financing Agency Revenue, 6.0%, 10/1/28                   1,695,510

                    Virginia  - 1.4%
1000000    BBB/Baa3 Peninsula Ports Authority, 6.0%, 4/1/33                                                          1,044,830
4000000    BB/NR    Pocahontas Parkway Association of Virginia Toll Road Revenue, 5.5%, 8/15/28                      3,832,000
                                                                                                                     4,876,830
                    Washington - 5.5%
4710000    AAA/Aaa  Spokane Public Facilities District Hotel/Motel Tax & Sales, 5.75%, 12/1/27                       5,455,687
7025000    BBB/Baa3 Tobacco Settlement Authority Washington, 6.625%, 6/1/32                                          7,071,014
14315000   AAA/Aaa  Washington State General Obligation, 0.0%, 6/1/22                                                6,387,639
                                                                                                                     18,914,340
Principal  S&P/Moody's
Amount     Ratings                                                                                                    Value
                    Wyoming - 1.5%
5000000    BB+/Ba3  Sweetwater County Solid Waste Disposal Revenue, 6.9%, 9/1/24                                     5,074,550

                    TOTAL TAX-EXEMPT OBLIGATIONS
                    (Cost $405,193,884)                                                                           433,986,023

Shares              TAX-EXEMPT MONEY MARKET MUTUAL FUND - 0.3% of Net Assets
1112083             BlackRock Provident Institutional Municipal Fund                                                 1,112,083
                    TOTAL TAX-EXEMPT MONEY MARKET MUTUAL FUND
                    (Cost $1,112,083)                                                                                1,112,083

                    TOTAL INVESTMENTS IN SECURITIES - 126.7%
                    (Cost $406,305,967) (c) (d)                                                                   435,098,106
                    OTHER ASSETS AND LIABILITIES -  2.7%                                                             9,399,908
                    PREFERRED SHARES AT REDEMPETION VALUE - (29.4)%                                              (101,000,000)
                    NET ASSETS APPLICABLE TO COMMON SHAREOWNERS - 100.0%                                         343,498,014

NR:                 Security not rated by S&P or Moody's.

(144A)              Security is exempt from registration under Rule 144A of the Securities Act of 1933.  Such
                    securities may be resold normally to qualified institutional buyers in a transaction exempt
                    from registration.  At January 31, 2005 the value of these securities amounted to
                    $977,600 or 0.3% of net assets applicable to common shareholders.

 +                  Prerefunded bonds have been collaterized by cash sufficient
                    to pay interest and principal  on the tax exempt issue and to
                    retire the bonds in full at the earliest refunding date.

 ++                 Prerefunded bonds have been collaterized by U.S. Treasury securities which
                    are held in escrow  to pay interest and principal
                    on the tax exempt issue and to retire the bonds in full at the earliest refunding date.

(a)                 Indicates a security that has a zero coupon that remains in effect until a
                     predetermined date at which time the
                    stated coupon rate becomes effective until final maturity.

(b)                 Security is in default and is non-incoming producing.

(c)                 The concentration of investments by type of obligation/market sector is as follows:
                    Insured                                                                                           15.3
                    General Obligation                                                                                1.8
                    Revenue Bonds:
                                        Health Revenue                                                                24.5
                                        Airport Revenue                                                               17.2
                                        Tobacco Revenue                                                               10.1
                                        Education Revenue                                                             7.1
                                        Pollution Control Revenue                                                     6.8
                                        Development Revenue                                                           5.9
                                        Power Revenue                                                                 4.4
                                        Transportation Revenue                                                        1.6
                                        Housing Revenue                                                               1.5
                                        Other                                                                         1.3
                                        Gaming Revenue                                                                1.2
                                        Facilities Revenue                                                            1.1
                                        Utilities Revenue                                                             0.2
                                                                                                                      100

(d)     (b)         At January 31, 2005, the net unrealized gain on investments based on cost
                    for federal income tax purposes of $405,495,705 was as follows:

        (e)         Aggregate gross unrealized gain for all investments in which
                    there is an excess of value over tax cost                                                         36933078

        (f)         Aggregate gross unrealized loss for all investments in which
                    there is an excess of tax cost over value                                                         -7330677
                    Net unrealized gain                                                                               29602401

                   For financial reporting purposes net unrealized gain on investments was 
                  $28,792,139 and cost of investments aggregated $406,305,967

                  The interest rate swaps outstanding as of January 31, 2005 were as follows:
Termination           Notional             Fixed                        Unrealized
Counterparty            Date         Amount (000)        Rate
UBS AG          April 5, 2009      $50,000          2.665%   1 month BMA  $552,500


ITEM 2. CONTROLS AND PROCEDURES.

(a) Disclose the conclusions of the registrant's principal executive officer or
officers and principal financial officer or officers, or persons performing
similar functions, about the effectiveness of the registrant's disclosure
controls and procedures (as defined in Rule 30a-3(c) under the Act (17 CFR
270.30a-3(c))) as of a date within 90 days of the filing date of the report
that includes the disclosure required by this paragraph, based on their
evaluation of these controls and procedures required by Rule 30a-3(b)
under the Act (17 CFR270.30a-3(b))) and Rule 13a-15(b) or 15d-15(b)
under the Exchange Act (17 CFR240.13a-15(b) or 240.15d-15(b)).

The registrant's certifying officers have determined that the registrant's
disclosure controls and procedures are effective based on an evaluation of
these controls and procedures as of a date within 90 days prior to the filing
date of this report.

(b) Disclose any change in the registrant's internal controls over financial
reporting (as defined in Rule 30a-3(d) under the Act (17 CFR270.30a-3(d)) 
that occurred during the registrant's last fiscal quarter that has materially
affected, or is reasonably likely to materially affect, the registrant's
internal control over financial reporting.

There was no significant change in the registrant's internal controls over
financial reporting that occurred during the registrant's last fiscal quarter
that has materially affected, or is reasonably likely to materially affect, 
the registrant's internal control over financial reporting. 



ITEM 3. EXHIBITS.

(a) A separate certification for each principal executive officer and principal
financial officer of the registrant as required by Rule 30a-2 under the Act
(17 CFR 270.30a-2).

Filed herewith.






                                   SIGNATURES

                          [See General Instruction F]


Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.


(Registrant) Pioneer  Municipal High Income Trust Fund;

By (Signature and Title)* /s/ John F. Cogan, Jr.
John F. Cogan, Jr, President

Date March 30, 2005


Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.


By (Signature and Title)* /s/ John F. Cogan, Jr.
John F. Cogan, Jr., President

Date March 30, 2005


By (Signature and Title)* /s/ Vincent Nave
Vincent Nave, Treasurer

Date March 30, 2005

* Print the name and title of each signing officer under his or her signature.