<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM 10-Q
                                    ---------

(Mark one)

    X     QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
   ---              SECURITIES EXCHANGE ACT OF 1934
                         

                  For the quarterly period ended MARCH 31, 1998
                                                 --------------

                                       OR

          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 0-2517


                          TOREADOR ROYALTY CORPORATION
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)
  

         Delaware                                             75-0991164
-------------------------------                           ------------------
(State or other jurisdiction of                            (I.R.S. Employer
incorporation or organization)                          Identification Number)

     530 Preston Commons West
       8117 Preston Road
          Dallas, Texas                                          75225
----------------------------------------                         -----
(Address of principal executive offices)                       (Zip Code)

Registrant's telephone number, including area code:  (214) 369-0080
                                                     --------------

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 twelve months, and (2) has been subject to such filing
requirements for the past 90 days.
                           Yes  X      No   
                               ---         ---                            

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

           Class                                 Outstanding at March 31, 1998
-------------------------------                  -----------------------------
Common Stock, $.15625 par value                           4,985,771



<PAGE>   2


                          PART I. FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

TOREADOR ROYALTY CORPORATION

CONSOLIDATED BALANCE SHEET

<TABLE>
<CAPTION>

                                                      March 31,      December 31,
                                                        1998            1997
                                                     -----------     ------------
                                                     (Unaudited)
<S>                                                  <C>             <C>        
ASSETS
Current Assets:
    Cash and cash equivalents                        $ 2,961,261     $ 2,876,652
    Accounts receivable                                  330,133         334,851
    Federal income tax receivable                         33,795          62,307
    Deferred tax benefit                                    --            15,945
    Other current assets                                  21,438          26,956
                                                     -----------     -----------

      Total current assets                             3,346,627       3,316,711
                                                     -----------     -----------

Properties, plant and equipment, less accumulated
        depreciation, depletion and amortization       3,385,983       3,210,074
                                                     -----------     -----------

      Total assets                                   $ 6,732,610     $ 6,526,785
                                                     ===========     ===========

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
    Accounts payable and accrued liabilities         $   213,963     $   309,590
    Federal income taxes payable                            --              --
                                                     -----------     -----------

      Total current liabilities                          213,963         309,590

Deferred tax liabilities                                  48,785            --
                                                     -----------     -----------
      Total liabilities                                  262,748         309,590
                                                     -----------     -----------

Stockholders' equity:
    Preferred stock, $1.00 par value, 4,000,000
        shares authorized; none issued                      --              --
    Common stock, $.15625 par value, 10,000,000
        shares authorized; 5,424,171 shares
        and 5,367,571 shares issued                      847,527         838,683
    Capital in excess of par value                     3,803,754       3,646,834
    Retained earnings                                  2,973,270       2,791,117
                                                     -----------     -----------
                                                       7,624,551       7,276,634
    Treasury stock at cost:  438,400 shares
        and 408,400 shares                            (1,154,689)     (1,059,439)
                                                     -----------     -----------
      Total stockholders' equity                       6,469,862       6,217,195
                                                     -----------     -----------
      Total liabilities and stockholders' equity     $ 6,732,610     $ 6,526,785
                                                     ===========     ===========
</TABLE>


  The Company uses the successful efforts method of accounting for its oil and
      gas producing activities. See accompanying notes to the consolidated
                             financial statements.



                                      -2-

<PAGE>   3


TOREADOR ROYALTY CORPORATION

CONSOLIDATED STATEMENT OF OPERATIONS
(UNAUDITED)

<TABLE>
<CAPTION>

                                               For the Three Months Ended
                                                       March 31,
                                               --------------------------
                                                   1998          1997
                                               -----------    -----------
<S>                                             <C>           <C>       
Revenues:
    Oil and gas sales                           $  635,745    $  677,835
    Lease bonuses and rentals                      168,664       109,938
    Interest and other income                       40,316        37,377
                                                ----------    ----------

      Total revenues                               844,725       825,150

Costs and expenses:
    Lease operating expense                        168,713       138,215
    Dry holes and abandonments                      71,176        53,455
    Depreciation, depletion and amortization        92,775        57,588
    Geological and geophysical                      58,182        74,014
    General and administrative                     178,487       229,796
    Settlement of benefit plans                       --          29,171
                                                ----------    ----------

      Total costs and expenses                     569,333       582,239
                                                ----------    ----------

Income before federal income taxes                 275,392       242,911

Provision for federal income taxes                  93,242        77,959
                                                ----------    ----------

Net income                                      $  182,150    $  164,952
                                                ==========    ==========

Basic income per share                          $     0.04    $     0.03
                                                ==========    ==========

Diluted income per share                        $     0.04    $     0.03
                                                ==========    ==========

Weighted average shares outstanding:
    Basic                                        4,989,060     5,140,960
    Diluted                                      5,063,267     5,144,456

</TABLE>



        See accompanying notes to the consolidated financial statements.


                                      -3-

<PAGE>   4


TOREADOR ROYALTY CORPORATION

CONSOLIDATED STATEMENT OF CASH FLOWS
(UNAUDITED)

<TABLE>
<CAPTION>

                                                              For the Three Months Ended
                                                                       March 31,
                                                              ---------------------------
                                                                 1998            1997
                                                              -----------     -----------
<S>                                                           <C>             <C>        
Cash flows from operating activities:
    Net income                                                $   182,150     $   164,952
    Adjustments to reconcile net income to net
     cash provided by operating activities:
      Depreciation, depletion and amortization                     92,775          57,588
      Dry holes and abandonments                                   71,176          53,455
      Decrease in accounts receivable                               4,718         266,689
      Decrease in federal income tax receivable                    28,512          54,899
      Increase in pension obligation                                 --           (19,546)
      Decrease in other current assets                              5,518           5,800
      Decrease in accounts payable and accrued liabilities        (95,627)       (227,070)
      Decrease in federal income taxes payable                       --            (1,263)
      Deferred tax expense                                         64,730          22,912
                                                              -----------     -----------
        Net cash provided by operating activities                 353,952         378,416
                                                              -----------     -----------

Cash flows from investing activities:
      Expenditures for oil and gas property and equipment        (340,860)        (95,757)
      Proceeds from lease bonuses and rentals                        --            77,635
                                                              -----------     -----------

        Net cash used by investing activities                    (340,860)        (18,122)
                                                              -----------     -----------

Cash flows from financing activities:
      Sale of stock                                               166,761            --
      Purchase of treasury stock                                  (95,250)        (11,826)
                                                              -----------     -----------

        Net cash provided (used) by financing activities           71,511         (11,826)
                                                              -----------     -----------


Net increase in cash and cash equivalents                          84,603         348,468

Cash and cash equivalents, beginning of period                  2,876,652       3,074,111
                                                              -----------     -----------

Cash and cash equivalents, end of period                      $ 2,961,255     $ 3,422,579
                                                              ===========     ===========

Supplemental schedule of cash flow information:
   Cash paid during the period for:
     Income taxes                                             $      --       $     1,411
</TABLE>





        See accompanying notes to the consolidated financial statements.


                                      -4-

<PAGE>   5



                          TOREADOR ROYALTY CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                    For the three months ended March 31, 1998

NOTE 1 - SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

         These consolidated financial statements should be read in the context
of the consolidated financial statements and notes thereto filed with the
Securities and Exchange Commission in Toreador Royalty Corporation's (the
"Company") 1997 Annual Report on Form 10-K. In the opinion of the Company, the
information furnished herein reflects all adjustments consisting of only normal
recurring adjustments, necessary for a fair presentation of the results of the
interim periods reported herein. Operating results from the interim period may
not necessarily be indicative of the results for the year ended December 31,
1998. Certain previously reported financial information has been reclassified to
conform to the current period's presentation.

NOTE 2 - NON-PRODUCING MINERAL AND ROYALTY INTERESTS

         Principal properties include mineral fee interests acquired by the
Company during 1951 and 1958. These interests totaled approximately 530,000 net
mineral acres underlying approximately 870,000 surface acres in the Texas
Panhandle and West Texas. It is recognized that the ultimate realization of the
investment in these properties is dependent upon future exploration and
development operations which are dependent upon satisfactory leasing and
drilling arrangements with others. Additionally, the Company owns working or
royalty interests in Texas, New Mexico, Oklahoma, Arkansas, Louisiana and
Colorado.

NOTE 3 - INTEREST AND OTHER INCOME

         Items in interest and other income consist of:

<TABLE>
<CAPTION>

                                                   Three Months Ended
                                                       March 31,
                                                   ------------------
                                                    1998       1997
                                                   -------    -------
<S>                                                <C>        <C>    
Interest                                           $37,226    $36,233
Other Income                                         3,090      1,144
                                                   -------    -------
                                                   $40,316    $37,377
                                                   =======    =======

</TABLE>

NOTE 4 - COMPREHENSIVE INCOME

         Effective January 1, 1998, the Company adopted Statement of Financial
Accounting Standard No. 130, "Reporting Comprehensive Income." The adoption of
this Statement had no effect on the Company's financial statements for the
quarters ended March 31, 1998 and 1997 as it has no items, other than net
income, which are considered in the determination of comprehensive income.



                                      -5-


<PAGE>   6



                          TOREADOR ROYALTY CORPORATION

                    For the three months ended March 31, 1998

ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
         CONDITION AND RESULTS OF OPERATIONS

         Disclosures Regarding Forward-Looking Statements

         This report on Form 10-Q includes "forward-looking statements" within
the meaning of Section 27A of the Securities Act of 1933, as amended, and
Section 21E of the Securities Exchange Act of 1934, as amended. All statements
other than statements of historical facts included in this Form 10-Q, including,
without limitation, statements contained in this "Management's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the
Company's financial position, business strategy, plans and objectives of
management of the Company for future operations, and industry conditions, are
forward-looking statements. Although the Company believes that the expectations
reflected in such forward-looking statements are reasonable, it can give no
assurance that such expectations will prove to have been correct. Any
forward-looking statements herein are subject to certain risks and uncertainties
inherent in petroleum exploration, development and production, including, but
not limited to the risk that no commercially productive oil and gas reservoirs
will be encountered; inconclusive results from 3-D seismic projects; delays or
cancellation of drilling operations as a result of a variety of factors;
volatility of oil and gas prices due to economic and other conditions; intense
competition in the oil and gas industry; operational risks (e.g., fires,
explosions, blowouts, cratering and loss of production); insurance coverage
limitations and requirements; and potential liability imposed by intense
governmental regulation of oil and gas production; all of which are beyond the
control of the Company. Any one or more of these factors could cause actual
results to differ materially from those expressed in any forward-looking
statement. All subsequent written and oral forward-looking statements
attributable to the Company or persons acting on its behalf are expressly
qualified in their entirety by the cautionary statements disclosed in this
paragraph and otherwise in this report.

         Liquidity and Capital Resources

         Historically, most of the exploration activity on the Company's acreage
has been funded and conducted by other oil companies. Exploration activity
typically generates lease bonus and option income to the Company. If drilling is
successful, the Company receives royalty income from the oil or gas production
but bears none of the capital or operating costs. In order to accelerate the
evaluation of its acreage as well as increase its ownership in any reserves
discovered, the Company has increased and intends to further increase its level
of participation in exploring its acreage by acquiring working interests. The
extent to which the Company may acquire working interests will depend on the
availability of outside capital and cash flow from operations. Currently, the
primary sources of capital for the financing of the Company's operations are
cash flows from operations. In November 1997, the Company obtained a $10 million
credit facility from Compass Bank with an initial availability of $4 million
which it may use to fund acquisition



                                      -6-

<PAGE>   7



                          TOREADOR ROYALTY CORPORATION

                    For the three months ended March 31, 1998

ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
         CONDITION AND RESULTS OF OPERATIONS (CONTINUED)

and development of oil and gas properties. The Company has not drawn any amounts
under the facility. In addition, the Company may reinvest proceeds from option
and lease bonuses by taking a working interest in 3-D seismic projects or in
wells. To the extent cash flow from operations does not significantly increase
and external sources of capital are limited or unavailable, the Company's
ability to make the capital investment to participate in 3-D seismic surveys and
increase its interest in projects on its acreage will be limited. Future funds
are expected to be provided through production from existing producing
properties and new producing properties that may be discovered through
exploration of the Company's acreage by third parties or by the Company itself.
Funds may also be provided through external financing in the form of debt or
equity. There can be no assurances as to the extent and availability of these
sources of funding.

         In September 1997, the Company engaged Dain Rauscher Wessels (formerly
Rauscher Pierce Refsnes, Inc.) as its financial advisor in evaluating strategic
alternatives available to the Company, including a sale of the Company, a merger
with another company and other forms of business combinations. The consummation
of any such transaction could result in a material increase or decrease in the
Company's liquidity, depending on the structure of the transaction. As of the
date of this report, the Company is not aware of any demands, commitments or
events which will result in its liquidity increasing or decreasing in a material
way. The Company presently has no debt and maintains its excess cash funds in
interest-bearing deposits. From time to time, the Company may receive lease
bonuses that cannot be anticipated and, when funds are available, the Company
may elect to participate in exploratory ventures. The Company also may acquire
producing oil and gas assets which could require the use of debt.

         Management believes that sufficient funds are available internally to
meet anticipated capital requirements for fiscal 1998.

         The Company has used $1,137,946 of its cash reserves to purchase
432,700 shares of its Common Stock, as of March 31, 1998. These purchases were
made pursuant to stock repurchase programs authorized by the Board of Directors
on October 10, 1995, of up to 100,000 shares of Common Stock, a second stock
repurchase program on April 22, 1996, of up to 150,000 shares of common stock
and a third stock repurchase program on April 21, 1997, of up to 300,000 shares
of common stock. As of May 12, 1998, the Company had purchased an aggregate of
182,700 shares at a purchase price of $506,918 under the third repurchase
program. The repurchases of the Company's shares of Common Stock were made in
unsolicited open-market purchases, at market (not premium) prices, without fixed
terms and not contingent upon the tender of a fixed minimum number of shares or
in response to a third party bid and otherwise in accordance with Rule 10b-18
under the Securities Exchange Act of 1934, as amended.



                                      -7-

<PAGE>   8



                          TOREADOR ROYALTY CORPORATION

                    For the three months ended March 31, 1998

ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
         CONDITION AND RESULTS OF OPERATIONS (CONTINUED)

RESULTS OF OPERATIONS

   THREE MONTHS ENDED MARCH 31, 1998 VS.
      THREE MONTHS ENDED MARCH 31, 1997

         Revenues for the first quarter of 1998 were $844,725 versus $825,150
for the same period in 1997. Oil and gas sales were $635,745 on volumes of
19,977 Bbls of oil and 147,656 Mcf of natural gas as compared to $677,835 on
volumes of 17,859 Bbls and 79,323 Mcf in 1997. The decrease of $42,090 in oil
and gas sales reflects lower oil and gas prices outweighing higher oil and gas
volumes. Oil volumes increased 11.9% primarily reflecting the Company's
participation in the exploratory drilling programs that occurred on its minerals
in the fourth quarter of 1997 and, in part, the first quarter of 1998. Gas
volumes increased 86.1% reflecting the acquisition of some gas properties in
mid-1997 and production increases from some older properties. The average price
on oil sales decreased 32.7% to $15.33/Bbl in 1998 compared to $22.79/Bbl in
1997. Likewise, the average price for gas sales decreased 34.6% to $2.23/Mcf in
1998 from $3.41/Mcf in 1997. Lease bonuses and rentals increased to $168,664 in
1998 versus $109,938 in 1997. Interest and other income was $40,316 in 1998 up
from $37,377 in 1997.

         Costs and expenses for the first quarter of 1998 were $569,333 in 1998
versus $582,239 for the same period in 1997. Lease operating expenses increased
to $168,713 in 1998 from $138,215 in 1997 due to the Company's increased level
of participation in the exploratory drilling programs on its minerals in the
fourth quarter of 1997 and an acquisition of producing oil and gas properties
made in 1997. Dry holes and abandonments increased to $71,176 in 1998 from
$53,455 in 1997. Depreciation, depletion and amortization increased 61.1% to
$92,775 in 1998 from $57,588 in 1997, reflecting the Company's continued level
of participation in the exploratory drilling programs on its minerals and a
downward revision to the proved developed reserves as of December 31, 1997,
created by a combination of some under-performing properties and lower oil and
gas prices. Geological and geophysical expenses decreased 21.4% to $58,182 in
1998 from $74,014 in 1997, reflecting a reduction in consulting engineering
expenses. Excluding the settlement of benefit plans, general and administrative
expenses decreased 22.3% to $178,487 from $229,796 a year ago, primarily
reflecting a reduction in salaries.

         The Company recognized net income of $182,150, or $0.04 per share
(basic), for the first quarter of 1998 versus net income of $164,952, or $0.03
per share (basic), for the same period in 1997.


                                      -8-


<PAGE>   9




                          TOREADOR ROYALTY CORPORATION

                                 March 31, 1998

                           PART II. OTHER INFORMATION

ITEM 5.   OTHER INFORMATION

         On April 27, 1998, the Company announced that it is actively seeking
acquisition and merger partners through its financial advisor, Dain Rauscher
Wessels. Toreador plans to continue its ongoing business if no satisfactory
proposal emerges.

ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K.

         (a)   Exhibits

         The information required by this Item 6(a) is set forth in the Index to
Exhibits accompanying this quarterly report and is incorporated herein by
reference.

         (b)   Reports on Form 8-K

         None.


                                   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.

                                        TOREADOR ROYALTY CORPORATION,
                                                Registrant



                                        /S/     John Mark McLaughlin
                                        ---------------------------------------
                                                John Mark McLaughlin,
                                                Chairman and President


May 12, 1998



                                      -9-


<PAGE>   10


                          TOREADOR ROYALTY CORPORATION

                                 March 31, 1998

                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>

      Exhibit
      Number                         Exhibits
     ---------    -------------------------------------------------------------

    <S>          <C>                                  
        27        -   Financial Data Schedule
        99        -   Press Release dated April 27, 1998
</TABLE>







                                      -10-