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

                                   FORM N-Q

                   QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS
    OF REGISTERED MANAGEMENT INVESTMENT COMPANY



                    Investment Company Act file number 811-21321


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


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


            Terrence J. Cullen, 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:  April 30

Date of reporting period:  January 31, 2016

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 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5).  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.


<PAGE>
ITEM 1. Schedule of Investments.

File the schedules as of the close of the reporting period as set forth in
ss. 210.12-12  12-14 of Regulation S-X [17 CFR 210.12-12  12-14]. The
schedules need not be audited.

 ITEM 2. CONTROLS AND PROCEDURES.

(a) Disclose the conclusions of the registrant's principal executive
and principal financial officers, or persons performing similar functions,
regarding 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 the
evaluation of these controls and procedures required by Rule 30a-3(b)
under the Act (17 CFR 270.30a-3(b))) and Rule 13a-15(b) or 15d-15(b)
under the Exchange Act (17 CFR 240.13a-15(b) or 240.15d-15(b)).

The registrant's principal executive officer and principal financial officer
have concluded that the registrant's disclosure controls and procedures are
effective based on their evaluation of these controls and procedures as of
a date within 90 days of 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 CFR 270.30a-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 were no significant changes in the registrant's internal control over
financial reporting that occurred during the second fiscal quarter of the
period covered by this report that have materially affected, or are
reasonably likely to materially affect, the registrant's internal control
over financial reporting.



ITEM 3. EXHIBITS.

File as exhibits as part of this Form a separate certification for each principal
executive officer and principal financial officer of the registrant as required
by Rule 30a-2(a) under the Act (17 CFR 270.30a-2(a)), exactly as set forth below:

                             CERTIFICATIONS

I, [identify the certifying individual], certify that:

1.  I have reviewed this report on Form N-Q of [identify registrant];

2.  Based on my knowledge, this report does not contain any untrue statement of
a material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3.  Based on my knowledge, the schedules of investments included in this report
fairly present in all material respects the investments of the registrant as of
the end of the fiscal quarter for which the report is filed;

4.  The registrants other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Rule 30a-3(c) under the Investment Company Act of 1940) and internal control over
financial reporting (as defined in Rule 30a-3(d) under the Investment Company Act
of 1940) for the registrant and have:

  (a)  Designed such disclosure controls and procedures, or caused such
  disclosure controls and procedures to be designed under our supervision, to
  ensure that material information relating to the registrant, including its
  consolidated subsidiaries, is made known to us by others within those entities,
  particularly during the period in which this report is being prepared;

  (b)  Designed such internal control over financial reporting, or caused such
  internal control over financial reporting to be designed under our supervision,
  to provide reasonable assurance regarding the reliability of financial
  reporting and the preparation of financial statements for external purposes
  in accordance with generally accepted accounting principles;

  (c)  Evaluated the effectiveness of the registrants disclosure controls and
  procedures and presented in this report our conclusions about the effectiveness
  of the disclosure controls and procedures, as of a date within 90 days prior to
  the filing date of this report, based on such evaluation; and

  (d)  Disclosed in this report any change in the registrants internal control
  over financial reporting that occurred during the registrants most recent
  fiscal quarter that has materially affected, or is reasonably likely to
  materially affect, the registrants internal control over financial reporting;
  and

5.  The registrants other certifying officer(s) and I have disclosed to the
registrants auditors and the audit committee of the registrants board of
directors (or persons performing the equivalent functions):

  (a)  All significant deficiencies and material weaknesses in the design or operation
  of internal control over financial reporting which are reasonably likely to adversely
  affect the registrants ability to record, process, summarize, and report financial
  information; and

  (b)  Any fraud, whether or not material, that involves management or other employees
  who have a significant role in the registrants internal control over financial
  reporting.


Date:                                                  [Signature] [Title]


Filed herewith.



<PAGE>


                                   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

By (Signature and Title)* /s/ Lisa M.Jones
                          -----------------------
                          Lisa M.Jones, President and Chief Executive Officer

Date March 30, 2016

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/ Lisa M.Jones
                          -----------------------
                          Lisa M.Jones, President and Chief Executive Officer


Date March 30, 2016



By (Signature and Title)* /s/ Mark E. Bradley
                          -----------------
                          Mark E. Bradley, Treasurer and Chief Accounting
                                        and Financial Officer

Date March 30, 2016

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