<PAGE>   1

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



                                    FORM 10-Q

              [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                  FOR THE QUARTERLY PERIOD ENDED MARCH 31, 2001

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
              FOR THE TRANSITION PERIOD FROM _________ TO ________

                          COMMISSION FILE NUMBER 1-8033

                           PERMIAN BASIN ROYALTY TRUST
           (EXACT NAME OF REGISTRANT AS SPECIFIED IN THE PERMIAN BASIN
                            ROYALTY TRUST INDENTURE)

           Texas                                         75-6280532
(State or Other Jurisdiction of             (I.R.S. Employer Identification No.)
Incorporation or Organization)


                              Bank of America, N.A.
                                Trust Department
                                 P.O. Box 830650
                               Dallas, Texas 75202
                         (Address of Principal Executive
                               Offices; Zip Code)

                                 (214) 209-2400
              (Registrant's Telephone Number, Including Area Code)

         Indicate by check mark whether the registrant: (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days. Yes [X] No [ ]

         Number of Units of beneficial interest of the Trust outstanding at May
1, 2001: 46,608,796.




<PAGE>   2

                           PERMIAN BASIN ROYALTY TRUST

                         PART I - FINANCIAL INFORMATION


ITEM 1. FINANCIAL STATEMENTS

The condensed financial statements included herein have been prepared by Bank of
America, N.A. as Trustee for the Permian Basin Royalty Trust, without audit,
pursuant to the rules and regulations of the Securities and Exchange Commission.
Certain information and footnote disclosures normally included in annual
financial statements have been condensed or omitted pursuant to such rules and
regulations, although the Trustee believes that the disclosures are adequate to
make the information presented not misleading. It is suggested that these
condensed financial statements be read in conjunction with the financial
statements and the notes thereto included in the Trust's latest annual report on
Form 10-K. In the opinion of the Trustee, all adjustments, consisting only of
normal recurring adjustments, necessary to present fairly the assets,
liabilities and trust corpus of the Permian Basin Royalty Trust at March 31,
2001, and the distributable income and changes in trust corpus for the
three-month periods ended March 31, 2001 and 2000 have been included. The
distributable income for such interim periods is not necessarily indicative of
the distributable income for the full year.

Deloitte & Touche LLP, independent certified public accountants, has made a
limited review of the condensed financial statements as of March 31, 2001 and
for the three-month periods ended March 31, 2001 and 2000 included herein.



                                       2
<PAGE>   3



                         INDEPENDENT ACCOUNTANTS' REPORT


Bank of America, N.A.,
         as Trustee for the Permian Basin Royalty Trust

We have reviewed the accompanying condensed statement of assets, liabilities and
trust corpus of the Permian Basin Royalty Trust as of March 31, 2001 and the
related condensed statements of distributable income and changes in trust corpus
for the three-month periods ended March 31, 2001 and 2000. These financial
statements are the responsibility of the Trustee.

We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures to
financial data and making inquiries of persons responsible for financial and
accounting matters. It is substantially less in scope than an audit conducted in
accordance with auditing standards generally accepted in the United States of
America, the objective of which is the expression of an opinion regarding the
financial statements taken as a whole. Accordingly, we do not express such an
opinion.

The accompanying condensed financial statements are prepared on a modified cash
basis as described in Note 1, which is a comprehensive basis of accounting other
than accounting principles generally accepted in the United States of America.

Based on our reviews, we are not aware of any material modifications that should
be made to such condensed financial statements for them to be in conformity with
the basis of accounting described in Note 1.

We have previously audited, in accordance with auditing standards generally
accepted in the United States of America, the statement of assets, liabilities
and trust corpus of the Permian Basin Royalty Trust as of December 31, 2000, and
the related statements of distributable income and changes in trust corpus for
the year then ended (not presented herein); and in our report dated March 20,
2001, we expressed an unqualified opinion on those financial statements. In our
opinion, the information set forth in the accompanying condensed statement of
assets, liabilities and trust corpus as of December 31, 2000 is fairly stated,
in all material respects, in relation to the statement of assets, liabilities
and trust corpus from which it has been derived.


/s/  DELOITTE & TOUCHE LLP


Dallas, Texas
May 4, 2001



                                       3
<PAGE>   4



PERMIAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

<TABLE>
<CAPTION>

                                                                                     March 31,       December 31,
                                                                                       2001              2000
                                                                                    ------------     ------------
                                                                                    (Unaudited)
<S>                                                                                 <C>              <C>
ASSETS

Cash and short-term investments                                                     $  4,294,102     $  3,056,122

Net overriding royalty interests in producing oil and gas properties (net of
    accumulated amortization of $8,438,214 and $8,379,962 at March 31, 2001 and
    December 31, 2000, respectively)                                                $  2,537,002     $  2,595,254
                                                                                    ------------     ------------

TOTAL ASSETS                                                                        $  6,831,104     $  5,651,376
                                                                                    ============     ============

LIABILITIES AND TRUST CORPUS

Distribution payable to Unit holders                                                $  4,294,102     $  3,056,122

Commitments and contingencies
Trust corpus - 46,608,796 Units of
    beneficial interest authorized and
    outstanding                                                                     $  2,537,002     $  2,595,254
                                                                                    ============     ============

TOTAL LIABILITIES
      AND TRUST CORPUS                                                              $  6,831,104     $  5,651,376
                                                                                    ============     ============
</TABLE>


The accompanying notes are an integral part of these financial statements.


                                       4


<PAGE>   5



PERMIAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)


<TABLE>
<CAPTION>

                                            THREE MONTHS    THREE MONTHS
                                               ENDED            ENDED
                                           March 31, 2001   March 31, 2000
                                           --------------   --------------
<S>                                         <C>              <C>
Royalty income                              $ 12,092,419     $  6,373,057
Interest income                                   26,177           16,829
                                            ------------     ------------
                                              12,118,596        6,389,886

General and administrative expenditures          165,982          123,821
                                            ------------     ------------

Distributable income                        $ 11,952,614     $  6,266,065
                                            ============     ============

Distributable income per Unit
    (46,608,796 Units)                      $        .26     $        .13
                                            ============     ============
</TABLE>


The accompanying notes to condensed financial statements are an integral part
of these statements.



                                       5

<PAGE>   6



PERMIAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF CHANGES IN TRUST CORPUS (UNAUDITED)

<TABLE>
<CAPTION>

                                             THREE MONTHS        THREE MONTHS
                                                ENDED               ENDED
                                            March 31, 2001      March 31, 2000
                                            --------------      --------------

<S>                                         <C>                 <C>
Trust corpus, beginning of period           $    2,595,254      $    2,889,978

Amortization of net overriding royalty
    interests                                      (58,252)            (78,525)
Distributable income                            11,952,614           6,266,065
Distributions declared                         (11,952,614)         (6,266,065)
                                            --------------      --------------
Trust Corpus, end of period                 $    2,537,002      $    2,811,453
                                            ==============      ==============

Distributions per unit                      $          .26      $          .13
                                            ==============      ==============
</TABLE>






                                       6



<PAGE>   7



PERMIAN BASIN ROYALTY TRUST

NOTES TO CONDENSED FINANCIAL STATEMENTS (UNAUDITED)


1.   BASIS OF ACCOUNTING

     The Permian Basin Royalty Trust ("Trust") was established as of November 1,
     1980. The net overriding royalties conveyed to the Trust include: (1) a 75%
     net overriding royalty carved out of Southland Royalty Company's fee
     mineral interests in the Waddell ranch in Crane County, Texas (the "Waddell
     Ranch properties"); and (2) a 95% net overriding royalty carved out of
     Southland Royalty Company's major producing royalty interests in Texas (the
     "Texas Royalty properties"). The net overriding royalty for the Texas
     Royalty properties is subject to the provisions of the lease agreements
     under which such royalties were created. The financial statements of the
     Trust are prepared on the following basis:

     o    Royalty income recorded for a month is the amount computed and paid to
          Bank of America, N.A. ("Trustee") as Trustee for the Trust by the
          interest owners: Burlington Resources Oil & Gas Company ("BROG") for
          the Waddell Ranch properties and Riverhill Energy Corporation
          ("Riverhill Energy"), formerly a wholly owned subsidiary of Riverhill
          Capital Corporation ("Riverhill Capital") and formerly an affiliate of
          Coastal Management Corporation ("CMC"), for the Texas Royalty
          properties. CMC currently conducts all field, technical and accounting
          operations on behalf of BROG with regard to the Waddell Ranch
          properties. CMC also conducts the accounting operations for the Texas
          Royalty properties on behalf of Riverhill Energy. Royalty income
          consists of the amounts received by the owners of the interest
          burdened by the net overriding royalty interests ("Royalties") from
          the sale of production less accrued production costs, development and
          drilling costs, applicable taxes, operating charges, and other costs
          and deductions multiplied by 75% in the case of the Waddell Ranch
          properties and 95% in the case of the Texas Royalty properties.

          As was previously reported, in February 1997, BROG sold its interest
          in the Texas Royalty properties to Riverhill Energy.

          The Trustee has been advised that in the first quarter of 1998,
          Schlumberger Technology Corporation ("Schlumberger") acquired all of
          the shares of stock of Riverhill Capital. Prior to such acquisition by
          Schlumberger, CMC and Riverhill Energy were wholly owned subsidiaries
          of Riverhill Capital. The Trustee has further been advised that in
          connection with Schlumberger's acquisition of Riverhill Capital, the
          shareholders of Riverhill Capital acquired ownership of all of the
          shares of stock of Riverhill Energy. Thus, the ownership in the Texas
          Royalty properties referenced above remained in Riverhill Energy, the
          stock ownership of which was acquired by the former shareholders of
          Riverhill Capital.

     o    Trust expenses recorded are based on liabilities paid and cash
          reserves established out of cash received or borrowed funds for
          liabilities and contingencies.



                                       7
<PAGE>   8

     o    Distributions to Unit holders are recorded when declared by the
          Trustee.

     o    Royalty income is computed separately for each of the conveyances
          under which the Royalties were conveyed to the Trust. If monthly costs
          exceed revenues for any conveyance ("excess costs"), such excess
          cannot reduce royalty income from other conveyances, but is carried
          forward with accrued interest to be recovered from future net proceeds
          of that conveyance.

     The financial statements of the Trust differ from financial statements
     prepared in accordance with accounting principles generally accepted in the
     United States of America ("GAAP") because revenues are not accrued in the
     month of production and certain cash reserves may be established for
     contingencies which would not be accrued in financial statements.
     Amortization of the Royalties calculated on a unit-of-production basis is
     charged directly to trust corpus.

2.   FEDERAL INCOME TAXES

     For Federal income tax purposes, the Trust constitutes a fixed investment
     trust which is taxed as a grantor trust. A grantor trust is not subject to
     tax at the trust level. The Unit holders are considered to own the Trust's
     income and principal as though no trust were in existence. The income of
     the Trust is deemed to have been received or accrued by each Unit holder at
     the time such income is received or accrued by the Trust and not when
     distributed by the Trust.

     The Royalties constitute "economic interests" in oil and gas properties for
     Federal income tax purposes. Unit holders must report their share of the
     revenues from the Royalties as ordinary income from oil and gas royalties
     and are entitled to claim depletion with respect to such income.

     The Trust has on file technical advice memoranda confirming the tax
     treatment described above.

     The classification of the Trust's income for purposes of the passive loss
     rules may be important to a Unit holder. As a result of the Tax Reform Act
     of 1986, royalty income will generally be treated as portfolio income and
     will not offset passive losses.





                                       8
<PAGE>   9

ITEM 2. TRUSTEE'S DISCUSSION AND ANALYSIS

FORWARD LOOKING INFORMATION

Certain information included in this report contains, and other materials filed
or to be filed by the Trust with the Securities and Exchange Commission (as well
as information included in oral statements or other written statements made or
to be made by the Trust) may contain or include, forward looking statements
within the meaning of Section 21E of the Securities Exchange Act of 1934, as
amended, and Section 27A of the Securities Act of 1933, as amended. Such forward
looking statements may be or may concern, among other things, capital
expenditures, drilling activity, development activities, production efforts and
volumes, hydrocarbon prices and the results thereof, and regulatory matters.
Although the Trustee believes that the expectations reflected in such
forward-looking statements are reasonable, such expectations are subject to
numerous risks and uncertainties and the Trustee can give no assurance that they
will prove correct. There are many factors, none of which is within the
Trustee's control, that may cause such expectations not to be realized,
including, among other things, factors such as actual oil and gas prices and the
recoverability of reserves, capital expenditures, general economic conditions,
actions and policies of petroleum-producing nations and other changes in the
domestic and international energy markets. Such forward looking statements
generally are accompanied by words such as "estimate," "expect," "predict,"
"anticipate," "goal," "should," "assume," "believe," or other words that convey
the uncertainty of future events or outcomes.

THREE MONTHS ENDED MARCH 31, 2001 COMPARED TO THREE MONTHS ENDED MARCH 31, 2000

For the quarter ended March 31, 2001 royalty income received by the Trust
amounted to $12,092,419 compared to royalty income of $6,373,057 during the
first quarter of 2000. The increase in royalty income is primarily attributable
to significant increases in both oil and gas prices.

Interest income for the quarter ended March 31, 2001, was $26,177 compared to
$16,829 during the first quarter of 2000. The increase in interest income is
primarily attributable to more funds available for investment. General and
administrative expenses during the first quarter of 2001 amounted to $165,982
compared to $123,821 during the first quarter of 2000. The increase in general
and administrative expenses can be primarily attributed to the timing of payment
of year end expenses.

These transactions resulted in distributable income for the quarter ended March
31, 2001 of $11,952,614, or $.256443 per Unit of beneficial interest.
Distributions of $.077108, $.087205 and $.092130 per Unit were made to Unit
holders of record as of January 31, February 28 and March 31, 2001,
respectively. For the first quarter of 2000, distributable income was
$6,266,065, or $.134440 per Unit of beneficial interest.

Royalty income for the Trust for the first quarter of the calendar year is
associated with actual oil and gas production for the period November and
December of 2000 and January 2001 from the properties from which the Trust's net
overriding royalty interests ("Royalties") were carved. Oil and gas sales
attributable to the Royalties and the properties from which the Royalties were
carved are as follows:


                                       9
<PAGE>   10

<TABLE>
<CAPTION>

                                                              FIRST QUARTER
                                                     -----------------------------
                                                         2001             2000
                                                     ------------     ------------
<S>                                                  <C>              <C>
ROYALTIES:
Oil sales (Bbls)                                          227,230          198,848
Gas sales (Mcf)                                           927,704          720,243

PROPERTIES FROM WHICH THE ROYALTIES WERE CARVED:
Oil:
    Total oil sales (Bbls)                                382,186          375,389
    Average per day (Bbls)                                  4,154            4,080
    Average price per Bbl                            $      27.90     $      23.64

Gas:
    Total gas sales (Mcf)                               1,590,793        1,519,812
    Average per day (Mcf)                                  17,291           16,520
    Average price per Mcf                            $       6.69     $       2.89
</TABLE>


The posted price of oil increased to an average price per barrel of $27.90 per
Bbl in the first quarter of 2001, compared to $23.64 per Bbl in the first
quarter of 2000. The Trustee has been advised by BROG that for the period August
1, 1993, through March 31, 2001, the oil from the Waddell Ranch properties was
being sold under a competitive bid to a third party. The average price of gas
increased from $2.89 per Mcf in the first quarter of 2000 to $6.69 per Mcf in
the first quarter of 2001.

Since the oil and gas sales attributable to the Royalties are based on an
allocation formula that is dependent on such factors as price and cost
(including capital expenditures), the production amounts in the Royalties
section of the above table do not provide a meaningful comparison. Oil and gas
sales volumes from the Underlying Properties increased for the applicable period
in 2001 compared to 2000.

Capital expenditures for drilling, remedial and maintenance activities on the
Waddell Ranch properties during the first quarter of 2001 totaled $2,379,000 as
compared to $1,717,000 for the first quarter of 2000. BROG has informed the
Trustee that the 2001 capital expenditures budget has been revised to $4.6
million for the Waddell Ranch. The total amount of capital expenditures for 2000
was $4.6 million. Through the first quarter of 2001, capital expenditures of
$2.4 million have been expended.

The Trustee has been advised that there were no wells completed and 10 wells in
progress during the three months ended March 31, 2001 or three months ended
March 31, 2000 on the Waddell Ranch properties.

Lease operating expense and property taxes totaled $2.7 million for the first
quarter of 2001, compared to $2.9 million in the first quarter of 2000 on the
Waddell Ranch properties. This decrease is primarily attributable to lower
maintenance costs for the quarter.




                                       10
<PAGE>   11

CALCULATION OF ROYALTY INCOME

The Trust's royalty income is computed as a percentage of the net profit from
the operation of the properties in which the Trust owns net overriding royalty
interests. These percentages of net profits are 75% and 95% in the case of the
Waddell Ranch properties and the Texas Royalty properties, respectively. Royalty
income received by the Trust for the three months ended March 31, 2001 and 2000,
respectively, were computed as shown in the table below:

<TABLE>
<CAPTION>

                                                                  THREE MONTHS ENDED MARCH 31,
                                                  --------------------------------------------------------------
                                                             2001                               2000
                                                  ----------------------------      ----------------------------
                                                   WADDELL           TEXAS           WADDELL           TEXAS
                                                    RANCH           ROYALTY           RANCH           ROYALTY
                                                  PROPERTIES       PROPERTIES       PROPERTIES       PROPERTIES
                                                  -----------      -----------      -----------      -----------
<S>                                               <C>              <C>              <C>              <C>
Gross proceeds of sales from the
    Underlying Properties
    Oil proceeds                                  $ 7,949,466      $ 2,824,057      $ 6,825,062      $ 2,048,059
    Gas proceeds                                    9,741,084        1,021,186        3,715,046          682,670
                                                  -----------      -----------      -----------      -----------
                      Total                        17,690,550        3,845,243       10,540,108        2,730,729
                                                  -----------      -----------      -----------      -----------

Less:
    Severance tax:
        Oil                                           333,403          117,774          277,353           78,399
        Gas                                           634,962           56,519          235,367           26,117
    Lease operating expense and property tax:
        Oil and gas                                 2,679,260          150,000        2,949,873          150,000
    Capital expenditures                            2,379,570              -0-        1,716,642              -0-
                                                  -----------      -----------      -----------      -----------
                      Total                         6,027,195          324,293        5,179,235          254,516
                                                  -----------      -----------      -----------      -----------

Net profits                                        11,663,355        3,520,950        5,360,873        2,476,213
Net overriding royalty interests                           75%              95%              75%              95%
                                                  -----------      -----------      -----------      -----------
Royalty income                                    $ 8,747,516      $ 3,344,903      $ 4,020,655      $ 2,352,402
                                                  ===========      ===========      ===========      ===========
</TABLE>


ITEM 3. QUALITATIVE AND QUANTITATIVE DISCLOSURES ABOUT MARKET RISK

Not applicable.



                                       11
<PAGE>   12



                           PART II - OTHER INFORMATION


ITEMS 1 THROUGH 5.

Not applicable.


ITEM 6.       EXHIBITS AND REPORTS ON FORM 8-K

              (a) Exhibits

                  (4)(a)   Permian Basin Royalty Trust Indenture dated November
                           3, 1980, between Southland Royalty Company (now
                           Burlington Resources Oil & Gas Company) and The First
                           National Bank of Fort Worth (now Bank of America,
                           N.A.), as Trustee, heretofore filed as Exhibit (4)(a)
                           to the Trust's Annual Report on Form 10-K to the
                           Securities and Exchange Commission for the fiscal
                           year ended December 31, 1980 is incorporated herein
                           by reference.

                  (4)(b)   Net Overriding Royalty Conveyance (Permian Basin
                           Royalty Trust) from Southland Royalty Company (now
                           Burlington Resources Oil & Gas Company) to The First
                           National Bank of Fort Worth (now Bank of America,
                           N.A.), as Trustee, dated November 3, 1980 (without
                           Schedules), heretofore filed as Exhibit (4)(b) to the
                           Trust's Annual Report on Form 10-K to the Securities
                           and Exchange Commission for the fiscal year ended
                           December 31, 1980 is incorporated herein by
                           reference.

                  (4)(c)   Net Overriding Royalty Conveyance (Permian Basin
                           Royalty Trust - Waddell Ranch) from Southland Royalty
                           Company (now Burlington Resources Oil & Gas Company)
                           to The First National Bank of Fort Worth (now Bank of
                           America, N.A.), as Trustee, dated November 3, 1980
                           (without Schedules), heretofore filed as Exhibit
                           (4)(c) to the Trust's Annual Report on Form 10-K to
                           the Securities and Exchange Commission for the fiscal
                           year ended December 31, 1980 is incorporated herein
                           by reference.

              (b) Reports on Form 8-K

                  No reports were filed during the quarter ended March 31, 2001.



                                       12
<PAGE>   13



                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                            BANK OF AMERICA, N.A.,
                                                TRUSTEE FOR THE
                                                PERMIAN BASIN ROYALTY TRUST




                                            By    /s/ RON E. HOOPER
                                              ----------------------------------
                                                  Ron E. Hooper
                                                  Senior Vice President

Date:  May 11, 2001


               (The Trust has no directors or executive officers.)


                                       13
<PAGE>   14



                                INDEX TO EXHIBITS




<TABLE>
<CAPTION>

                 EXHIBIT
                  NUMBER               DESCRIPTION
                  ------               -----------
<S>                        <C>
                  (4)(a)   Permian Basin Royalty Trust Indenture dated November
                           3, 1980, between Southland Royalty Company (now
                           Burlington Resources Oil & Gas Company) and The First
                           National Bank of Fort Worth (now Bank of America,
                           N.A.), as Trustee, heretofore filed as Exhibit (4)(a)
                           to the Trust's Annual Report on Form 10-K to the
                           Securities and Exchange Commission for the fiscal
                           year ended December 31, 1980 is incorporated herein
                           by reference.*

                  (b)      Net Overriding Royalty Conveyance (Permian Basin
                           Royalty Trust) from Southland Royalty Company (now
                           Burlington Resources Oil & Gas Company) to The First
                           National Bank of Fort Worth (now Bank of America,
                           N.A.), as Trustee, dated November 3, 1980 (without
                           Schedules), heretofore filed as Exhibit (4)(b) to the
                           Trust's Annual Report on Form 10-K to the Securities
                           and Exchange Commission for the fiscal year ended
                           December 31, 1980 is incorporated herein by
                           reference.*

                  (c)      Net Overriding Royalty Conveyance (Permian Basin
                           Royalty Trust - Waddell Ranch) from Southland Royalty
                           Company (now Burlington Resources Oil & Gas Company)
                           to The First National Bank of Fort Worth (now Bank of
                           America, N.A.), as Trustee, dated November 3, 1980
                           (without Schedules), heretofore filed as Exhibit
                           (4)(c) to the Trust's Annual Report on Form 10-K to
                           the Securities and Exchange Commission for the fiscal
                           year ended December 31, 1980 is incorporated herein
                           by reference.*
</TABLE>

*   A copy of this Exhibit is available to any Unit holder, at the actual cost
    of reproduction, upon written request to the Trustee, Bank of America, N.A.,
    P. O. Box 830650, Dallas, Texas 75202.



                                       14