<PAGE>   1

                                                                    EXHIBIT 10.2


                                                            FINAL EXECUTION COPY

                          TOREADOR ROYALTY CORPORATION

                          STOCKHOLDER VOTING AGREEMENT


         This STOCKHOLDER VOTING AGREEMENT, dated June 25, 1998 (the
"Agreement") is made and entered into by and among Mr. G. Thomas Graves, III and
Mr. William I. Lee, individuals whose business address is 4809 Cole Avenue,
Suite 107, Dallas, Texas 75205, Lee Global Energy Fund, L.P., a Texas limited
partnership ("Lee Global"), Gralee Capital Corp., a Texas corporation ("Gralee
Capital"), and Gralee Partners, L.P., a Texas limited partnership ("Gralee
Partners" and together with Mr. Graves, Mr. Lee, Lee Global and Gralee Capital,
collectively referred to as the "Gralee Persons"); Mr. Peter Lawrence Falb and
Mr. Edward Nathan Dane, individuals whose business address is 33 Broad Street,
Boston, Massachusetts 02109, Firethorn I Limited Partnership, a Massachusetts
limited partnership ("Firethorn"), the Hilary Bell Falb 1983 Trust (the "HBF
Trust"), the Alison Forslund Falb 1985 Trust (the "AFF Trust"), the Forslund
Irrevocable Trust (the "Forslund Trust"), and Dane, Falb, Stone & Co., Inc., a
Massachusetts corporation ("Dane Falb" and, together with Mr. Falb, Mr. Dane,
the HBF Trust, the AFF Trust, the Forslund Trust and Firethorn, collectively
referred to as the "Dane Falb Persons"); and Mr. John V. Ballard, an individual
whose address is 161-A Heritage Hills, Somers, New York 10589, Mr. J. W.
Bullion, an individual whose business address is 1700 Pacific Avenue, Suite
3300, Dallas, Texas 75201, Mr. Thomas P. Kellogg, an individual whose business
address is 50 Horseshoe Road, Darien, Connecticut 06820, Mr. John Mark
McLaughlin, an individual whose business address is 2201 Sherwood Way, Suite
213, San Angelo, Texas 76901, Mr. Peter R. Vig, an individual whose business
address is 101 Park Avenue, 48th Floor, New York, New York 10178, and Mr. Jack
L. Woods, an individual whose business address is 294 North Bay Drive, Bullard,
Texas 75757 (collectively referred to as "Current Management") (each of the
persons constituting the Gralee Persons, the Dane Falb Persons and Current
Management are sometimes collectively referred to as the "Stockholders").

                              W I T N E S S E T H:

         WHEREAS, each of the Stockholders is a holder of shares of Common Stock
(as defined) of Toreador Royalty Corporation, a Delaware corporation (the
"Company");

         NOW, THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein the parties to this Agreement hereby agree as
follows:

         1. Definitions of Certain Agreement Terms. For purposes of this
Agreement, the terms hereinafter set forth shall have the following definitions
unless otherwise specifically stated:

         "1998 Annual Meeting" means the 1998 annual meeting of stockholders of
the Company at which the election of directors shall be considered.



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         "1999 Annual Meeting" means the 1999 annual meeting of stockholders of
the Company at which the election of directors shall be considered.

         "2000 Annual Meeting" means the 2000 annual meeting of stockholders of
the Company at which the election of directors shall be considered.

         "Board" means the Board of Directors of the Company.

         "Bylaws" means the Amended and Restated Bylaws of the Company as
hereinafter amended or supplemented.

         "Common Stock" means the common stock, par value $.15625 per share, of
the Company.

         "Company Nominating Committee" shall mean the continuing director
nominating committee of the Board as established pursuant to the Bylaws.

         "Company Securities" means any securities issued by the Company,
including the Common Stock and any other debt or equity securities of the
Company that are outstanding as of the date hereof or may hereafter be issued.

         "Dane Falb Schedule 13D" means the Statement on Schedule 13D filed with
the SEC on April 7, 1995 by Mr. Falb, Mr. Dane, Firethorn and Dane Falb, as
amended through Amendment No. 5 thereto dated May 5, 1998.

         "Effective Period" shall mean the period commencing immediately
subsequent to the 1998 Annual Meeting and ending on the earlier to occur of (i)
such time as (x) the Gralee Persons are no longer the beneficial owners in the
aggregate of at least 514,677 shares of Common Stock, and (y) the Dane Falb
Persons are no longer the beneficial owners in the aggregate of at least 514,677
shares of Common Stock, and (ii) the day immediately subsequent to the 2000
Annual Meeting.

         "Exchange Act" means the Securities Exchange Act of 1934, as amended.

         "Falb Nominating Committee" shall mean the Falb nominating committee of
the Board as established pursuant to the Bylaws.

         "Gralee Nominating Committee" shall mean the Gralee nominating
committee of the Board as established pursuant to the Bylaws.

         "Lee Global Schedule 13D" means the Statement on Schedule 13D filed
with the SEC on June 2, 1997 by Lee Global, as amended through Amendment No. 3
thereto dated April 28, 1998.

         "Person" means any individual, corporation, association, general or
limited partnership, limited liability company, limited liability partnership,
joint venture, trust, estate, other entity or organization or group.


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         "Rights Agreement" means the rights agreement dated as of April 3, 1995
between the Company and Continental Stock Transfer & Trust Company, as rights
agent, as amended or supplemented.

         "SEC" means the United States Securities and Exchange Commission.

         The terms "participant," "proxy" and "solicitation" shall be used as
defined in Regulation 14A under the Exchange Act. The terms "beneficial
ownership" and "group" shall be used as defined in Regulation 13D-G under the
Exchange Act. The terms "affiliate" and "associate" shall be used as defined in
Rule 12b-2 under the Exchange Act.

         2. Nominations to the Company's Board of Directors at the 1998 Annual
Meeting.

                  (a) The Stockholders agree that they will support the
nomination and the election of the following seven (7) nominees standing for
election at the 1998 Annual Meeting to serve on the Board until the 1999 Annual
Meeting and until their respective successors shall be duly elected and
qualified: J. W. Bullion, current director of the Company; Thomas P. Kellogg,
Jr., current director of the Company; and John Mark McLaughlin, current director
of the Company (collectively referred to as the "Company Designees"); G. Thomas
Graves, III and William I. Lee (collectively referred to as the "Gralee
Designees"); and Peter Lawrence Falb and Edward Nathan Dane (collectively
referred to as the "Dane Falb Designees"). The Gralee Persons and the Dane Falb
Persons shall cause the Gralee Designees and the Dane Falb Designees,
respectively, to consent to serving as members of the Board, and provide the
biographical, beneficial ownership of Common Stock and other information
required to be disclosed in the Company's proxy materials used for the
solicitation of proxies at the 1998 Annual Meeting.

                  (b) Each Stockholder shall vote (including the taking of any
action by written consent, as necessary or appropriate), and shall cause its
affiliates to vote (including the taking of any action by written consent, as
necessary or appropriate), all shares of Common Stock which they are entitled to
vote (or control the voting of, directly or indirectly) at the 1998 Annual
Meeting in favor of the election of the nominees set forth in subsection (a) of
this Section 2.

         3. Nominations to the Company's Board of Directors at the 1999 Annual
Meeting and 2000 Annual Meeting. During the Effective Period, the Stockholders
agree as follows:

                  (a) If the slate of nominees set forth in subsection (a) of
Section 2 are willing and able to act as such at the 1999 Annual Meeting and the
2000 Annual Meeting, the Stockholders shall support the nomination and election
of such seven nominees for election to the Board at the 1999 Annual Meeting and
the 2000 Annual Meeting.

                  (b) If one or more of the Company Designees declines or is
otherwise unable to stand as nominee(s) for the election of directors at the
1999 Annual Meeting or the 2000 Annual Meeting, then the Stockholders agree the
replacement nominee(s) shall be nominated by the Company Nominating Committee.
If one or more of the Gralee Designees declines or is

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otherwise unable to stand as nominee(s) for the election of directors at the
1999 Annual Meeting or the 2000 Annual Meeting, then the Stockholders agree the
replacement nominee(s) shall be nominated by the Gralee Nominating Committee. If
one or more of the Dane Falb Designees declines or is otherwise unable to stand
as nominee(s) for the election of directors at the 1999 Annual Meeting or the
2000 Annual Meeting, then the Stockholders agree the replacement nominee(s)
shall be nominated by the Falb Nominating Committee. The Stockholders shall
support the nomination and the election of the slate of nominees as selected in
accordance with this subsection (b) for election to the Board at the 1999 Annual
Meeting and the 2000 Annual Meeting.

                  (c) Each Stockholder shall vote (including the taking of any
action by written consent, as necessary or appropriate), and shall cause its
affiliates to vote (including the taking of any action by written consent, as
necessary or appropriate), all shares of Common Stock which they are entitled to
vote (or control the voting of, directly or indirectly) at the 1999 Annual
Meeting and the 2000 Annual Meeting in favor of the election of the nominees
selected in accordance with subsection (a) or (b) of this Section 3.

         4. Board Vacancies. During the Effective Period and notwithstanding any
provision of the Bylaws with respect to the filling of vacancies on the Board to
the contrary, the Stockholders agree to vote (including the taking of any action
by written consent, as necessary or appropriate), and shall cause its affiliates
to vote (including the taking of any action by written consent, as necessary or
appropriate), all shares of Common Stock which they are entitled to vote (or
control the voting of, directly or indirectly), and otherwise take commercially
reasonable actions to cause vacancies on the Board to be filled as follows:

                  (a) in the event that one or more of the Company Designees
ceases to serve as a member of the Board during his term of office but prior to
December 31, 2000, the resulting vacancy on the Board shall be filled by a
person nominated by the Company Nominating Committee.

                  (b) in the event that one or more of the Gralee Designees
ceases to serve as a member of the Board during his term of office but prior to
December 31, 2000, the resulting vacancy on the Board shall be filled by a
person nominated by the Gralee Nominating Committee.

                  (c) in the event that one or more of the Dane Falb Designees
ceases to serve as a member of the Board during his term of office but prior to
December 31, 2000, the resulting vacancy on the Board shall be filled by a
person nominated by the Falb Nominating Committee.

         5.       Covenants.

                  (a) The Gralee Persons and the Dane Falb Persons agree to
withdraw their demand for a stockholder list and related information dated April
9, 1998 and April 27, 1998, respectively.


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                  (b) Except as otherwise provided in this Agreement or as
agreed to by five (5) of the seven (7) members of the Board then in office, no
Stockholder or its affiliates will prior to December 31, 2000:

                          (i) (A) seek election to, or seek to place a
representative on, the Board, (B) engage in any solicitation of proxies with
respect to any Company Securities or (C) become a participant in any election
contest relating to the election of directors of the Company;

                          (ii) initiate, propose or otherwise solicit
stockholders of the Company, for the approval of one or more stockholder
proposals, as described in Rule 14a-8 under the Exchange Act, or otherwise;

                          (iii) vote in favor of or execute a consent with
respect to any matter or proposal submitted to the Company's stockholders by
vote or otherwise unless such matter or proposal has first been recommended to
stockholders by five (5) of the seven (7) members of the Board then in office,
and such recommendation has not been withdrawn; it being understood that the
Stockholders shall have no obligation to vote on any matter submitted to
stockholders other than as provided in Sections 2 and 3 hereof;

                          (iv) propose or seek to effect or seek permission of
the Board or stockholders of the Company to propose or effect on behalf of or
for the benefit of any Stockholder other than as a stockholder on an equal basis
(A) any form of business combination transaction involving the Company,
including without limitation a merger, consolidation, tender offer, share
exchange or exchange offer, (B) any sale of assets of the Company, (C) any
issuance or sale of equity securities of the Company or (D) any restructuring,
recapitalizing or similar transaction with respect to the Company;

                          (v) initiate, propose or otherwise solicit
stockholders to amend or terminate the Rights Agreement, or to redeem the rights
issued thereunder; or

                          (vi) aid, encourage or act in concert with any person,
firm, corporation, group or other entity to take any of the actions prohibited
by Section 5(b) hereof.

                  (c) With respect to Dane Falb discretionary accounts, the
covenants in Section 5(b) shall apply only insofar as Dane Falb exercises
discretionary authority with respect to Company Securities held in such
accounts.

         6. Representations and Warranties of the Gralee Persons. The Gralee
Persons jointly and severally represent and warrant to Current Management as
follows:

                  (a) Each Gralee Person has the power and authority to execute,
deliver and carry out the terms and provisions of this Agreement and to
consummate the transactions contemplated hereby, and has taken all necessary
action to authorize the execution, delivery and performance of this Agreement.


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<PAGE>   6


                  (b) This Agreement has been duly and validly authorized,
executed and delivered by each Gralee Person, and constitutes a valid and
binding obligation of each Gralee Person, enforceable in accordance with its
terms, subject to applicable bankruptcy, reorganization, insolvency or other
laws affecting the enforcement of creditors' rights generally.

                  (c) None of the Gralee Persons or any of its affiliates
beneficially owns, or has any direct, indirect or contingent pecuniary interest
in, any Company Securities other than as disclosed in the Lee Global Schedule
13D.

                  (d) None of the Gralee Persons or any of its respective
affiliates is a member of any group with respect to any Company Securities, and
there are no other persons who are part of such a group with it or any of its
affiliates, except as disclosed in the Lee Global Schedule 13D.

         7. Representations and Warranties of the Dane Falb Persons. The Dane
Falb Persons jointly and severally represent and warrant to Current Management
as follows:

                  (a) Each Dane Falb Person has the power and authority to
execute, deliver and carry out the terms and provisions of this Agreement and to
consummate the transactions contemplated hereby, and has taken all necessary
action to authorize the execution, delivery and performance of this Agreement.

                  (b) This Agreement has been duly and validly authorized,
executed and delivered by each Dane Falb Person, and constitutes a valid and
binding obligation of each Dane Falb Person, enforceable in accordance with its
terms, subject to applicable bankruptcy, reorganization, insolvency or other
laws affecting the enforcement of creditors' rights generally.

                  (c) Except for an aggregate of 14,500 shares of Common Stock
held by the HBF Trust, the AFF Trust and the Forslund Trust, none of the members
of the Dane Falb Persons or any of its affiliates beneficially owns, or has any
direct, indirect or contingent pecuniary interest in, any Company Securities
other than as disclosed in the Dane Falb Schedule 13D.

                  (d) None of the Dane Falb Persons or any of its respective
affiliates is a member of any group with respect to any Company Securities, and
there are no other persons who are part of such a group with it or any of its
affiliates, except as disclosed in the Dane Falb Schedule 13D.

         8. Representations and Warranties of Current Management Current
Management jointly and severally represents and warrants to the Gralee Persons
and the Dane Falb Persons as follows:

                  (a) Each member of Current Management has the power and
authority to execute, deliver and carry out the terms and provisions of this
Agreement and to consummate the transactions contemplated hereby, and has taken
all necessary action to authorize the execution, delivery and performance of
this Agreement.


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<PAGE>   7


                  (b) This Agreement has been duly and validly executed and
delivered by each member of Current Management, and constitutes a valid and
binding obligation of each member of Current Management, enforceable in
accordance with its terms, subject to applicable bankruptcy, reorganization,
insolvency or other laws affecting the enforcement of creditors' rights
generally.

         9. Successors, Assigns and Transferees. Subject to applicable laws
regarding the sale or transfer of Common Stock by the Stockholders, the terms
and provisions of this Agreement shall not be deemed to restrict or limit future
sales of Common Stock by the Stockholders. The terms and provisions of this
Agreement shall not bind, inure to the benefit of or be enforceable by or
against the successors, assigns or transferees of each of the Stockholders. No
Stockholder may assign its rights under this Agreement.

         10. Survival of Representations. All representations, warranties and
agreements made by the Stockholders in this Agreement or pursuant hereto shall
survive the date hereof.

         11. Entire Agreement; Amendments. This Agreement, including that
certain Agreement of even date herewith among the Gralee Persons, the Dane Falb
Persons, the Company, among other parties thereto, and such additional
instruments as may be concurrently executed and delivered pursuant to this
Agreement, constitutes the entire understanding of the parties with respect to
its subject matter. There are no restrictions, agreements, promises,
representations, warranties, covenants or undertakings other than those
expressly set forth herein or in the documents delivered concurrently herewith.
This Agreement may be amended only by a written instrument duly executed by all
the parties hereto.

         12. Headings. The section headings contained in this Agreement are for
reference purposes only and shall not effect in any way the meaning or
interpretation of this Agreement.

         13. Notices, All notices, requests, claims, demands and other
communications hereunder shall be in writing and shall be given (and shall be
deemed to have been duly given if so given) by hand delivery, facsimile or by
mail (registered or certified, postage prepaid, return receipt requested) to the
respective parties as follows:

                  If to the Gralee Persons:

                           Gralee Capital Corp.
                           4809 Cole Avenue
                           Suite 107
                           Dallas, Texas 75205
                           Attention:  Mr. G. Thomas Graves, III
                           Fax No:  (214) 521-8834


                                       -7-


<PAGE>   8



                  with a copy to:

                           Haynes & Boone, LLP
                           901 Main Street
                           Suite 3100
                           Dallas, Texas 75202
                           Attention:  Ms. Janice V. Sharry
                           Fax No:  (214) 651-5940

                  If to the Dane Falb Persons:

                           Dane, Falb, Stone & Co., Inc.
                           33 Broad Street
                           Boston, Massachusetts 02109
                           Attention: Mr. Peter Falb
                           Fax No:  (617) 742-2304

                  with a copy to:

                           Richards, Layton & Finger
                           920 King Street
                           Wilmington, Delaware 19801
                           Attn: Mr. Jesse Finkelstein
                           Fax No.: (302) 658-6548

                  and:

                           Choate, Hall & Stewart
                           Exchange Place
                           53 State Street
                           Boston, MA 02109
                           Attn: Ms. Carla Herwitz
                           Fax No.: (617) 248-4000

                  If to Current Management:

                           2201 Sherwood Way
                           Suite 213
                           San Angelo, Texas 76901
                           Attention: Mr. John Mark McLaughlin
                           Fax: (915) 949-0480


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                  with a copy to:

                           Thompson & Knight, P.C.
                           1700 Pacific Avenue
                           Suite 3300
                           Dallas, Texas 75201
                           Attention: Mr. Joe Dannenmaier
                           Fax: (214) 969-1751

or to such other address as the person to whom notice is given may have
previously furnished to the others in writing in the manner set forth above.

         14. Governing Law. This Agreement shall be governed by and construed
and enforced in accordance with the laws of the State of Delaware, without
reference to the conflict of laws principles thereof.

         15. Waiver. Any waiver by any party of a breach of any provision of
this Agreement shall not operate as or be construed to be a waiver of any other
breach of such provision or of any breach of any other provision of this
Agreement. The failure of a party to insist upon strict adherence to any term of
this Agreement on one or more occasions shall not be considered a waiver or
deprive that party of the right thereafter to insist upon strict adherence to
that term or any other term of this Agreement.

         16. Challenges to Agreement. Each party hereto shall not, and shall use
its best efforts to cause its affiliates, associates and representatives not to,
challenge the validity of any provisions of this Agreement. In the event that
any part of this Agreement or any transaction contemplated hereby is
temporarily, preliminarily or permanently enjoined or restrained by court of
competent jurisdiction, the parties hereto shall use their reasonable best
efforts to cause any such injunction or restraining order to be vacated or
dissolved or otherwise declared or determined to be of no further force or
effect.

         17. Specific Performance. Each of the Stockholders acknowledges and
agrees that irreparable harm would occur if any provision of this Agreement were
not performed in accordance with the terms thereof, or were otherwise breached,
and that such harm could not be remedied by an award of damages. Accordingly,
the Stockholders agree that any non-breaching Stockholder shall be entitled to
an injunction to prevent breaches of this Agreement and to enforce specifically
the terms and provisions hereof.

         18. Counterparts. This Agreement may be executed in counterparts, each
of which shall be an original, but each of which together shall constitute one
and the same Agreement.

                                    * * * * *


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         IN WITNESS WHEREOF, and intending to be legally bound hereby, each of
the undersigned parties has executed or caused this Agreement to be executed on
the date first above written.

                                  LEE GLOBAL ENERGY FUND, L.P.

                                  By: Gralee Partners, L.P., its general partner

                                      By: Gralee Capital Corp., its general
                                          partner

                                          By: /s/ G. T. Graves, III
                                             ----------------------------------
                                          Name: G. T. Graves, III
                                               --------------------------------
                                          Title: President
                                                -------------------------------

                                  GRALEE CAPITAL CORPORATION

                                  By: /s/ G. T. Graves, III
                                     ------------------------------------------
                                     Name: G. T. Graves, III
                                          -------------------------------------
                                     Title: President
                                           ------------------------------------

                                  GRALEE PARTNERS, L.P.

                                  By: Gralee Partners, L.P., its general partner

                                      By: /s/ G. T. Graves, III
                                         --------------------------------------
                                         Name: G. T. Graves, III
                                              ---------------------------------
                                         Title: President
                                               --------------------------------


                                   /s/ G. Thomas Graves, III
                                   ----------------------------------
                                   G. Thomas Graves, III

                                   /s/ Peter Lawrence Falb
                                   ----------------------------------
                                   Peter Lawrence Falb


                                   /s/ Edward Nathan Dane
                                   ----------------------------------
                                   Edward Nathan Dane



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                                   FIRETHORN I LIMITED PARTNERSHIP

                                   By: Firethorn II Limited Partnership, its 
                                       general partner

                                   By: Eaglerock Corporation, its general 
                                       partner

                                       By: /s/ PETER L. FALB
                                          -------------------------------------
                                          Name: Peter L. Falb
                                               --------------------------------
                                          Title: Treasurer 
                                                -------------------------------

                                   THE HILARY BELL FALB 1983 TRUST


                                   By: /s/ Karen F. Falb, Trustee
                                      -----------------------------------------
                                         Karen F. Falb, Trustee


                                   THE ALISON FORSLUND FALB 1985 TRUST


                                   By: /s/ Karen F. Falb, Trustee
                                      -----------------------------------------
                                       Karen F. Falb, Trustee



                                   DANE, FALB, STONE & CO., INC.


                                   By: /s/ PETER L. FALB
                                      -----------------------------------------
                                      Name: Peter L. Falb
                                           ------------------------------------
                                      Title: Principal
                                            -----------------------------------


                                   /s/ John V. Ballard
                                   ----------------------------------------
                                   John V. Ballard


                                   /s/ J.W. Bullion
                                   ---------------------------------------
                                   J.W. Bullion


                                   /s/ Thomas P. Kellogg, Jr.
                                   ---------------------------------------
                                   Thomas P. Kellogg, Jr.



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<PAGE>   12



                                      /s/ John Mark McLaughlin
                                      --------------------------------
                                      John Mark McLaughlin


                                      /s/ Peter R. Vig
                                      --------------------------------
                                      Peter R. Vig


                                      /s/ Jack L. Woods
                                      --------------------------------
                                      Jack L. Woods


                                      -12-


<PAGE>   13



                                      THE FORSLUND IRREVOCABLE TRUST


                                      By: /s/ Karen F. Falb, Trustee
                                          ----------------------------------
                                          Karen F. Falb, Trustee



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