<PAGE>   1
                                                                    EXHIBIT 99.1

                              LETTER OF TRANSMITTAL

                        Offer For Any and All Outstanding
                      9% Senior Subordinated Notes due 2007
                                 in Exchange for
                      9% Senior Subordinated Notes due 2007
           Which Have Been Registered Under The Securities Act of 1933
               Pursuant to the Prospectus dated November 10, 1997

THE EXCHANGE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., NEW YORK CITY
TIME, ON DECEMBER 12, 1997, UNLESS THE OFFER IS EXTENDED. TENDERS MAY BE
WITHDRAWN PRIOR TO 5:00 P.M., NEW YORK CITY TIME, ON THE EXPIRATION DATE.

                The Exchange Agent For The Exchange Offer Is:
                             The Bank Of New York

<TABLE>
<S>                                      <C>                                   <C>
By Hand Or Overnight Delivery              Facsimile Transmissions:            By Registered Or Certified Mail:
                                         (Eligible Institutions Only)

    The Bank of New York                                                              The Bank of New York
     101 Barclay Street                          (212)571-3080                        101 Barclay Street, 7E
Corporate Trust Services Window            New York, New York  10286
        Ground Level                         To Confirm by Telephone             Attention:  Reorganization Section,
Attention:  Reorganization Section,          or for Information Call

                                                  (212) 815-6333
</TABLE>


      Delivery of this letter of transmittal to an address other than as set
forth above or transmission of this letter of transmittal via facsimile to a
number other than as set forth above does not constitute a valid delivery.

      The undersigned acknowledges that he or she has received the Prospectus,
dated: November 10, 1997 (the "Prospectus"), of Giant Industries, Inc., a
Delaware corporation ("Giant"), and this Letter of Transmittal, which together
constitute Giant's offer (the "Exchange Offer") to exchange an aggregate
principal amount of up to $150,000,000 9% Senior Subordinated Notes due 2007,
which have been registered under the Securities Act of 1993, as amended (the
"Securities Act") (the "Exchange Notes") for a like principal amount of the
issued and outstanding 9% Senior Subordinated Notes due 2007 (the "Notes") of
the Company from the holders thereof.

      THE INSTRUCTIONS CONTAINED HEREIN SHOULD BE READ CAREFULLY BEFORE THIS
LETTER OF TRANSMITTAL IS COMPLETED.

      Capitalized terms used but not defined herein shall have the same meaning
given them in the Prospectus (as defined below).
<PAGE>   2
      This Letter of Transmittal is to be completed by holders of Notes either
if Notes are to be forwarded herewith or if tenders of Notes are to be made by
book-entry transfer to an account maintained by The Bank of New York (the
"Exchange Agent") at The Depository Trust Company (the "Book-Entry Transfer
Facility" or "DTC") pursuant to the procedures set forth in "The Registered
Exchange Offer -- Registered Exchange Offer Procedures" in the Prospectus.

      Holders of Notes whose certificates (the "Certificates") for such Notes
are not immediately available or who cannot deliver their Certificates and all
other required documents to the Exchange Agent on or prior to the Expiration
Date (as defined in the Prospectus) or who cannot complete the procedures for
book-entry transfers on a timely basis, must tender their Notes according to the
guaranteed delivery procedures set forth in "The Registered Exchange Offer --
Guaranteed Delivery Procedures" in the Prospectus.

      DELIVERY OF DOCUMENTS TO THE BOOK-ENTRY TRANSFER FACILITY DOES NOT
CONSTITUTE DELIVERY TO THE EXCHANGE AGENT.

                   NOTE: SIGNATURES MUST BE PROVIDED BELOW
             PLEASE READ THE ACCOMPANYING INSTRUCTIONS CAREFULLY

      The undersigned has completed the appropriate boxes below and signed this
Letter of Transmittal to indicate the action the undersigned desires to take
with respect to the Exchange Offer.

<TABLE>
<CAPTION>
<S>                                                      <C>                <C>              <C>
-------------------------------------------------------------------------------------------------------
               DESCRIPTION OF NOTES                          1                  2                3
-------------------------------------------------------------------------------------------------------
                                                                            Aggregate        Principal
                                                                            Principal        Amount of
 Name(s) and Address(es) of Registered Holder(s):        Certificate        Amount of          Notes
            (Please fill in, if blank)                   Number(s)*           Notes






                                                                                             Tendered**
-------------------------------------------------------------------------------------------------------

-------------------------------------------------------------------------------------------------------

-------------------------------------------------------------------------------------------------------
                                                         Total
-------------------------------------------------------------------------------------------------------
</TABLE>

*     Need not be completed if Notes are being tendered by book-entry holders.

**    Notes may be tendered in whole or in part in integral multiples of $1,000.
      See Instruction 4. Unless otherwise indicated in the column, a holder will
      be deemed to have tendered all Notes represented by Notes indicated in
      Column 2. See Instruction 4.


                                       2
<PAGE>   3
          (BOXES BELOW TO BE CHECKED BY ELIGIBLE INSTITUTIONS ONLY)


/ /         CHECK HERE IF TENDERED NOTES ARE BEING DELIVERED BY BOOKENTRY
            TRANSFER MADE TO THE ACCOUNT MAINTAINED BY THE EXCHANGE AGENT WITH
            THE BOOK-ENTRY TRANSFER FACILITY AND COMPLETE THE FOLLOWING:

            Name of Tendering Institution_______________________________________


            Account Number______________________________________________________

            Transaction Code Number_____________________________________________


/ /         CHECK HERE AND ENCLOSE A PHOTOCOPY OF THE NOTICE OF GUARANTEED
            DELIVERY IF TENDERED NOTES ARE BEING DELIVERED PURSUANT TO A NOTICE
            OF GUARANTEED DELIVERY PREVIOUSLY SENT TO THE EXCHANGE AGENT AND
            COMPLETE THE FOLLOWING:

            Name of Registered Holder(s)________________________________________

            Window Ticket Number (if any)_______________________________________

            Date of Execution of Notice of Guaranteed Delivery__________________

            Name of Institution which Guaranteed Delivery_______________________

                  If Guaranteed Delivery is to be made by Book-Entry Transfer:

            Name of Tendering Institution_______________________________________

            Account Number _____________________________________________________

            Transaction Code Number_____________________________________________

/ /         CHECK HERE IF TENDERED BY BOOK-ENTRY TRANSFER AND NON-EXCHANGED
            NOTES ARE TO BE RETURNED BY CREDITING THE BOOK-ENTRY TRANSFER
            FACILITY ACCOUNT NUMBER SET FORTH ABOVE.


                                       3
<PAGE>   4
/ /         CHECK HERE IF YOU ARE A BROKER-DEALER WHO ACQUIRED THE NOTES FOR ITS
            OWN ACCOUNT AS A RESULT OF MARKET MAKING OR OTHER TRADING ACTIVITIES
            (A "PARTICIPATING BROKER-DEALER") AND WISH TO RECEIVE 10 ADDITIONAL
            COPIES OF THE PROSPECTUS AND 10 COPIES OF ANY AMENDMENTS OR
            SUPPLEMENTS THERETO.

            Name: ______________________________________________________________

            Address: ___________________________________________________________


Ladies and Gentlemen:

      Upon the terms and subject to the conditions of the Exchange Offer, the
undersigned hereby tenders to Giant, the above-described aggregate principal
amount of the Company's Notes in exchange for a like aggregate principal amount
of the Company's Exchange Notes which have been registered under the Securities
Act upon the terms and subject to the conditions set forth in the Prospectus
dated November 10, 1997 (as the same may be amended or supplemented from time to
time, the "Prospectus"), receipt of which is acknowledged, and in this Letter of
Transmittal (which, together with the Prospectus, constitute the "Exchange
Offer").

      Subject to and effective upon the acceptance for exchange of all or any
portion of the Notes tendered herewith in accordance with the terms and
conditions of the Exchange Offer (including, if the Exchange Offer is extended
or amended, the terms and conditions of any such extension or amendment), the
undersigned hereby sells, assigns and transfers to or upon the order of Giant
all right, title and interest in and to such Notes as are being tendered
herewith. The undersigned hereby irrevocably constitutes and appoints the
Exchange Agent as its agent and attorney-in-fact (with full knowledge that the
Exchange Agent is also acting as agent of Giant in connection with the Exchange
Offer) with respect to the tendered Notes, with full power of substitution (such
power of attorney being deemed to be an irrevocable power coupled with an
interest) subject only to the right of withdrawal described in the Prospectus,
to (i) deliver Certificates for Notes to Giant together with all accompanying
evidences of transfer and authenticity to, or upon the order of, Giant, upon
receipt by the Exchange Agent, as the undersigned's agent, of the Exchange Notes
to be issued in exchange for such Notes, (ii) present Certificates for such
Notes for transfer, and to transfer the Notes on the books of Giant, and (iii)
receive for the account of Giant all benefits and otherwise exercise all rights
of beneficial ownership of such Notes, all in accordance with the terms and
conditions of the Exchange Offer.

      THE UNDERSIGNED HEREBY REPRESENTS AND WARRANTS THAT THE UNDERSIGNED HAS
FULL POWER AND AUTHORITY TO TENDER, EXCHANGE, SELL, ASSIGN AND TRANSFER THE
NOTES TENDERED HEREBY AND THAT, WHEN THE SAME ARE ACCEPTED FOR EXCHANGE, GIANT
WILL ACQUIRE GOOD, MARKETABLE AND UNENCUMBERED TITLE THERETO, FREE AND CLEAR OF
ALL LIENS, RESTRICTIONS, CHARGES AND ENCUMBRANCES, AND THAT THE NOTES TENDERED
HEREBY ARE NOT SUBJECT TO ANY ADVERSE CLAIMS OR PROXIES. THE UNDERSIGNED WILL,
UPON REQUEST, EXECUTE AND DELIVER ANY


                                       4
<PAGE>   5
ADDITIONAL DOCUMENTS DEEMED BY GIANT OR THE EXCHANGE AGENT TO BE NECESSARY OR
DESIRABLE TO COMPLETE THE EXCHANGE, ASSIGNMENT AND TRANSFER OF THE NOTES
TENDERED HEREBY, AND THE UNDERSIGNED WILL COMPLY WITH ITS OBLIGATIONS UNDER THE
REGISTRATION RIGHTS AGREEMENT. THE UNDERSIGNED HAS READ AND AGREES TO ALL OF THE
TERMS OF THE EXCHANGE OFFER.

      The name(s) and address(es) of the registered holder(s) of the Notes
tendered hereby should be printed above, if they are not already set forth
above, as they appear on the Certificates representing such Notes. The
Certificate number(s) and the Notes that the undersigned wishes to tender should
be indicated in the appropriate boxes above.

      If any tendered Notes are not exchanged pursuant to the Exchange Offer for
any reason, or if Certificates are submitted for more Notes than are tendered or
accepted for exchange, Certificates for such non-exchanged Notes will be
returned (or, in the case of Notes tendered by book-entry transfer, such Notes
will be credited to an account maintained at DTC), without expense to the
tendering holder, promptly following the expiration or termination of the
Exchange Offer.

      The undersigned understands that tenders of Notes pursuant to any one of
the procedures describe in "The Registered Exchange Offer -- Registered Exchange
Offer Procedure" in the Prospectus and in the instruction, attached hereto will,
upon Giant's acceptance for exchange of such tendered notes, constitute a
binding agreement between the undersigned and Giant upon the terms and subject
to the conditions of the Exchange Offer. The undersigned recognizes that, under
certain circumstances set forth in the Prospectus, Giant may not be required to
accept for exchange any of the Notes tendered hereby.

      Unless otherwise indicated herein in the box entitled "Special Issuance
Instructions" below, the undersigned hereby directs that the Exchange Notes be
issues in the name(s) of the undersigned or, in the case of a book-entry
transfer of Notes, that such Exchange Notes be credited to the account indicated
above maintained at DTC. If applicable, substitute Certificates representing
Notes not exchanged or not accepted for exchange will be issued to the
undersigned or, in the case of a book-entry transfer of Notes will be credited
to the account indicated above maintained at DTC. Similarly, unless otherwise
indicated under "Special Delivery Instructions," please deliver Exchange Notes
to the undersigned at the address shown below the undersigned's signature.

      BY TENDERING NOTES AND EXECUTING THIS LETTER OF TRANSMITTAL, THE
UNDERSIGNED HEREBY REPRESENTS AND AGREES THAT: (I) THE UNDERSIGNED IS NOT AN
"AFFILIATE" OF GIANT OR, IF IT IS SUCH AN AFFILIATE, THAT THE EXCHANGE NOTES MAY
NOT BE OFFERED FOR RESALE, RESOLD OR OTHERWISE TRANSFERRED WITHOUT REGISTRATION
UNDER AND COMPLIANCE WITH THE PROSPECTUS DELIVERY REQUIREMENT OF THE SECURITIES
ACT OR AN EXEMPTION THEREFROM; (II) ANY EXCHANGE NOTES TO BE RECEIVED BY THE
UNDERSIGNED ARE BEING ACQUIRED IN THE ORDINARY COURSE OF ITS BUSINESS; (III) THE
UNDERSIGNED HAS NO ARRANGEMENT OR UNDERSTANDING WITH ANY PERSON TO PARTICIPATE
IN A DISTRIBUTION (WITHIN THE MEANING OF THE SECURITIES ACT) OF EXCHANGE NOTES
TO BE RECEIVED IN THE


                                       5
<PAGE>   6
EXCHANGE OFFER; AND (IV) IF THE UNDERSIGNED IS NOT A BROKER-DEALER, THE
UNDERSIGNED IS NOT ENGAGED IN, AND DOES NOT INTEND TO ENGAGE IN, A DISTRIBUTION
(WITHIN THE MEANING OF THE SECURITIES ACT) OF SUCH NOTES. BY TENDERING NOTES
PURSUANT TO THE EXCHANGE OFFER AND EXECUTING THIS LETTER OF TRANSMITTAL, A
HOLDER OF NOTES WHICH IS A BROKER-DEALER REPRESENTS AND AGREES, CONSISTENT WITH
CERTAIN INTERPRETIVE LETTERS ISSUED BY THE STAFF OF THE DIVISION OF CORPORATION
FINANCE OF THE SECURITIES AND EXCHANGE COMMISSION TO THIRD PARTIES, THAT (A)
SUCH NOTES HELD BY THE BROKER-DEALER ARE HELD ONLY AS A NOMINEE, OR (B) SUCH
NOTES WERE ACQUIRED BY SUCH BROKER-DEALER FOR ITS OWN ACCOUNT AS A RESULT OF
MARKET-MAKING ACTIVITIES OR OTHER TRADING ACTIVITIES AND IT WILL DELIVER THE
PROSPECTUS (AS AMENDED OR SUPPLEMENTED FROM TIME TO TIME) MEETING THE
REQUIREMENTS OF THE SECURITIES ACT IN CONNECTION WITH ANY RESALE OF SUCH
EXCHANGE NOTES (PROVIDED THAT, BY SO ACKNOWLEDGING AND BY DELIVERING A
PROSPECTUS, SUCH BROKER-DEALER WILL NOT BE DEEMED TO ADMIT THAT IT IS AN
"UNDERWRITER" WITHIN THE MEANING OF THE SECURITIES ACT).

      GIANT HAS AGREED THAT, SUBJECT TO THE PROVISIONS OF THE REGISTRATION
RIGHTS AGREEMENT, THE PROSPECTUS, AS IT MAY BE AMENDED OR SUPPLEMENTED FROM TIME
TO TIME, MAY BE USED BY A PARTICIPATING BROKER-DEALER (AS DEFINED BELOW) IN
CONNECTION WITH RESALES OF EXCHANGE NOTES RECEIVED IN EXCHANGE FOR NOTES, WHERE
SUCH NOTES WERE ACQUIRED BY SUCH PARTICIPATING BROKER-DEALER FOR ITS OWN ACCOUNT
AS A RESULT OF MARKET-MAKING ACTIVITIES OR OTHER TRADING ACTIVITIES, FOR A
PERIOD ENDING 180 DAYS AFTER THE EXPIRATION DATE (SUBJECT TO EXTENSION UNDER
CERTAIN LIMITED CIRCUMSTANCES DESCRIBED IN THE PROSPECTUS) OR, IF EARLIER, WHEN
ALL SUCH EXCHANGE NOTES HAVE BEEN DISPOSED OF BY SUCH PARTICIPATING
BROKER-DEALER. IN THAT REGARD, EACH BROKER-DEALER WHO ACQUIRED NOTES FOR ITS OWN
ACCOUNT AS A RESULT OF MARKET-MAKING OR OTHER TRADING ACTIVITIES (A
"PARTICIPATING BROKER-DEALER"), BY TENDERING SUCH NOTES AND EXECUTING THIS
LETTER OF TRANSMITTAL, AGREES THAT, UPON RECEIPT OF NOTICE FROM GIANT OF THE
OCCURRENCE OF ANY EVENT OR THE DISCOVERY OF ANY FACT WHICH MAKES ANY STATEMENT
CONTAINED OR INCORPORATED BY REFERENCE IN THE PROSPECTUS UNTRUE IN ANY MATERIAL
RESPECT OR WHICH CAUSES THE PROSPECTUS TO OMIT TO STATE A MATERIAL FACT
NECESSARY IN ORDER TO MAKE THE STATEMENTS CONTAINED OR INCORPORATED BY REFERENCE
THEREIN, IN LIGHT OF THE CIRCUMSTANCES UNDER WHICH THEY WERE MADE, NOT
MISLEADING OR OF THE OCCURRENCE OF CERTAIN OTHER EVENTS SPECIFIED IN THE
REGISTRATION RIGHTS AGREEMENT, SUCH PARTICIPATING BROKER-DEALER WILL SUSPEND THE
SALE OF NOTES PURSUANT TO THE PROSPECTUS UNTIL GIANT HAS AMENDED OR SUPPLEMENTED
THE PROSPECTUS TO CORRECT SUCH MISSTATEMENT OR OMISSION AND HAS FURNISHED COPIES
OF THE AMENDED OR SUPPLEMENTED PROSPECTUS TO THE PARTICIPATING BROKER-DEALER OR
GIANT HAS GIVEN NOTICE THAT THE SALE OF EXCHANGE NOTES MAY BE RESUMED, AS THE
CASE


                                       6
<PAGE>   7
MAY BE. IF GIANT GIVES SUCH NOTICE TO SUSPEND THE SALE OF EXCHANGE NOTES, IT
SHALL EXTEND THE 180-DAY PERIOD REFERRED TO ABOVE DURING WHICH PARTICIPATING
BROKER-DEALERS ARE ENTITLED TO USE THE PROSPECTUS IN CONNECTION WITH THE RESALE
OF EXCHANGE NOTES BY THE NUMBER OF DAYS DURING THE PERIOD FROM AND INCLUDING THE
DATE OF THE GIVING OF SUCH NOTICE TO AND INCLUDING THE DATE WHEN PARTICIPATING
BROKER-DEALERS SHALL HAVE RECEIVED COPIES OF THE SUPPLEMENTED OR AMENDED
PROSPECTUS NECESSARY TO PERMIT RESALES OF EXCHANGE NOTES OR TO AND INCLUDING THE
DATE ON WHICH GIANT HAS GIVEN NOTICE THAT THE SALE OF EXCHANGE NOTES MAY BE
RESUMED, AS THE CASE MAY BE.

      Holders of Notes whose Notes are accepted for exchange will not receive
accrued interest on such Notes for any period from and after the last Interest
Payment Date to which interest has been paid or duly provided for on such Notes
prior to the original issue date of the Exchange Notes or, if no such interest
has been paid or duly provided for, will not receive any accrued interest on
such Notes, and the undersigned waives the right to receive any interest on such
Notes accrued from and after such Interest Payment Date or, if no such interest
has been paid or duly provided for, from and after August 26, 1997.

      The undersigned will, upon request, execute and deliver any additional
documents deemed by Giant to be necessary or desirable to complete the sale,
assignment and transfer of the Notes tendered hereby. All authority herein
conferred or agreed to be conferred in this Letter of Transmittal shall survive
the death or incapacity of the undersigned and any obligation of the undersigned
hereunder shall be binding upon the heirs, executors, administrators, personal
representatives, trustees in bankruptcy, legal representatives, successors and
assigns of the undersigned. Except as stated in the Prospectus, this tender is
irrevocable.

      THE UNDERSIGNED, BY COMPLETING THE BOX ENTITLED "DESCRIPTION OF NOTES"
ABOVE AND SIGNING THIS LETTER, WILL BE DEEMED TO HAVE TENDERED THE NOTES AS
SET FORTH IN SUCH BOX.


                                       7
<PAGE>   8
                               HOLDER(S) SIGN HERE
                          (SEE INSTRUCTIONS 2, 5 AND 6)
                (PLEASE COMPLETE SUBSTITUTE FORM W-9 ON PAGE 18)
      (NOTE: SIGNATURE(S) MUST BE GUARANTEED IF REQUIRED BY INSTRUCTION 2)

      Must be signed by registered holder(s) exactly as name(s) appear(s) on
Certificates(s) for the Notes hereby tendered or on the register of holders
maintained by or on behalf of Giant, or by any person(s) authorized to become
the registered holder(s) by endorsements and documents transmitted herewith
(including such opinions of counsel, certifications and other information as may
be required by Giant for the Notes to comply with the restrictions on transfer
applicable to the Notes). If signature is by an attorney-in-fact, executor,
administrator, trustee, guardian, officer of a corporation or another acting in
a fiduciary capacity or representative capacity, please set forth the signer's
full title. See Instruction 5.


________________________________________________________________________________

________________________________________________________________________________

                           (SIGNATURE(S) OF HOLDER(S))


Date:  _______________, 1997

Name(s)_________________________________________________________________________

       _________________________________________________________________________
                                (PLEASE PRINT)


Capacity (full title)___________________________________________________________

Address    _____________________________________________________________________
           _____________________________________________________________________
           _____________________________________________________________________
                              (INCLUDE ZIP CODE)

Area Code and Telephone Number__________________________________________________

________________________________________________________________________________
               (TAX IDENTIFICATION OR SOCIAL SECURITY NUMBER(S))


                                       8
<PAGE>   9
                          GUARANTEE OF SIGNATURE(S)
                          (SEE INSTRUCTIONS 2 AND 5)


________________________________________________________________________________
                            (AUTHORIZED SIGNATURE)


Date:  ________________, 1997

Name of Firm ___________________________________________________________________

      Capacity (full title)_____________________________________________________
                                            (PLEASE PRINT)

Address    _____________________________________________________________________
           _____________________________________________________________________
           _____________________________________________________________________
                              (INCLUDE ZIP CODE)

Area Code and Telephone Number__________________________________________________


                                       9
<PAGE>   10
                        SPECIAL ISSUANCE INSTRUCTIONS
                        (SEE INSTRUCTIONS 1, 5 AND 6)

To be completed ONLY if the Exchange Notes or Notes not tendered are to be
issued in the name of someone other than the registered holder of the Notes
whose name(s) appear(s) above.

Issue

/ /      Notes not tendered to:

/ /      Exchange Notes to:

Name(s)  _______________________________________________________________________

Address  _______________________________________________________________________

         _______________________________________________________________________
                               (INCLUDE ZIP CODE)

Area Code and
Telephone Number________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________
               (TAX IDENTIFICATION OR SOCIAL SECURITY NUMBERS)


                                       10
<PAGE>   11
                        SPECIAL DELIVERY INSTRUCTIONS
                        (SEE INSTRUCTIONS 1, 5 AND 6)

To be completed ONLY if Exchange Notes or Notes not tendered are to be sent to
someone other than the registered holder of Notes whose name(s) appear(s) above,
or such registered holder(s) at an address other than that shown above.

Mail

/ /      Notes not tendered to:

/ /      Exchange Notes to:

Name(s) ________________________________________________________________________

Address ________________________________________________________________________

        ________________________________________________________________________
                               (INCLUDE ZIP CODE)


Area Code and
Telephone Number _______________________________________________________________

________________________________________________________________________________
              (TAX IDENTIFICATION OR SOCIAL SECURITY NUMBER(S))


                                       11
<PAGE>   12
                                  INSTRUCTIONS

        FORMING PART OF THE TERMS AND CONDITIONS OF THE EXCHANGE OFFER

      1. DELIVERY OF LETTER OF TRANSMITTAL AND CERTIFICATES; GUARANTEED DELIVERY
PROCEDURES. This Letter of Transmittal is to be completed either if (a)
Certificates are to be forwarded herewith or (b) tenders are to be made pursuant
to the procedures for tender by book-entry transfer set forth in "The Registered
Exchange Offer -- Registered Exchange Offer Procedures" in the Prospectus.
Certificates, or timely confirmation of a book-entry transfer of such Notes into
the Exchange Agent's account at DTC, as well as this Letter of Transmittal (or
facsimile thereof), properly completed and duly executed, with any required
signature guarantees, and any other documents required by this Letter of
Transmittal, must be received by the Exchange Agent at its address set forth
herein on or prior to the Expiration Date. Notes may be tendered in whole or in
part in integral multiples of $1,000.

      Holders who wish to tender their Notes and (i) whose Notes are not
immediately available or (ii) who cannot deliver their Notes, this Letter of
Transmittal and all other required documents to the Exchange Agent on or prior
to the Expiration Date or (iii) who cannot complete the procedures for delivery
by book-entry transfer on a timely basis, may tender their Notes by properly
completing and duly executing a Notice of Guaranteed Delivery pursuant to the
guaranteed delivery procedures set forth in "The Registered Exchange Offer --
Guaranteed Delivery Procedures" in the Prospectus. Pursuant to such procedures:
(i) such tender must be made by or through an Eligible Institution (as defined
below); (ii) a properly completed and duly executed Notice of Guaranteed
Delivery, substantially in the form made available by the Company, must be
received by the Exchange Agent on or prior to the Expiration Date; and (iii) the
Certificates (or a book-entry confirmation (as defined in the Prospectus))
representing all tendered Notes, in proper form for transfer, together with a
Letter of Transmittal (or facsimile thereof), properly completed and duly
executed, with any required signature guarantees and any other documents
required by this Letter of Transmittal, must be received by the Exchange Agent
within three New York Stock Exchange, Inc. trading days after the Expiration
Date, all as provided in "The Registered Exchange Offer -- Guaranteed Delivery
Procedures for Tendering Notes" in the Prospectus.

      The Notice of Guaranteed Delivery may be delivered by hand or transmitted
by facsimile or mail to the Exchange Agent, and must include a guarantee by an
Eligible Institution in the form set forth in such Notice. For Notes to be
properly tendered pursuant to the guaranteed delivery procedure, the Exchange
Agent must receive a Notice of Guaranteed Delivery on or prior to the Expiration
Date. As used herein and in the Prospectus, "Eligible Institution" means a firm
or other entity identified in Rule 17Ad-15 under the Exchange Act as "an
eligible guarantor institution," including (as such terms are defined therein)
(i) a bank; (ii) a broker, dealer, municipal securities broker or dealer or
government securities broker or dealer; (iii) a credit union; (iv) a national
securities exchange, registered securities association or clearing agency; or
(v) a savings association that is a participant in a Securities Transfer
Association.

      THE METHOD OF DELIVERY OF CERTIFICATES, THIS LETTER OF TRANSMITTAL AND ALL
OTHER REQUIRED DOCUMENTS IS AT THE OPTION AND SOLE RISK OF THE TENDERED HOLDER
AND THE DELIVERY WILL BE DEEMED MADE ONLY WHEN ACTUALLY RECEIVED BY THE EXCHANGE
AGENT. IF


                                       12
<PAGE>   13
DELIVERY IS BY MAIL, REGISTERED MAIL WITH RETURN RECEIPT REQUESTED, PROPERLY
INSURED, OR OVERNIGHT DELIVERY SERVICE IS RECOMMENDED. IN ALL CASES, SUFFICIENT
TIME SHOULD BE ALLOWED TO ENSURE TIMELY DELIVERY. NO LETTER OF TRANSMITTAL,
NOTES OR OTHER REQUIRED DOCUMENTS SHOULD BE SENT TO GIANT.

      Giant will not accept any alternative, conditional or contingent tenders.
Each tendering holder, by execution of a Letter of Transmittal (or facsimile
thereof), waives any right to receive any notice of the acceptance of such
tender.

      2. GUARANTEE OF SIGNATURES. No signature guarantee on this Letter of
Transmittal is required if:

      (i)   this Letter of Transmittal is signed by the registered holder (which
            term, for purposes of this document, shall include any participant
            in DTC whose name appears on the register of holders maintained by
            or on behalf of Giant as the owner of the Notes) of Notes tendered
            herewith, unless such holder(s) has completed either the box
            entitled "Special Issuance Instructions" or the box entitled
            "Special Delivery Instructions" above, or

      (ii)  such Notes are tendered for the account of a firm that is an
            Eligible Institution.

      In all other cases, an Eligible Institution must guarantee the
signature(s) on this Letter of Transmittal.  See Instruction 5.

      3. INADEQUATE SPACE. If the space provided in the box captioned
"Description of Notes" is inadequate, the Certificate number(s) and/or the
principal amount of Notes and any other required information should be listed on
a separate signed schedule which is attached to this Letter of Transmittal.

      4. PARTIAL TENDERS AND WITHDRAWAL RIGHTS. Tenders of Notes will be
accepted only in integral multiples of $1,000. If less than all the Notes
evidenced by any Certificate submitted are to be tendered, fill in the principal
amount of Notes which are to be tendered in the box entitled "Liquidation Amount
of Notes Tendered (if less than all)." In such case, new Certificate(s) will
only be sent to the holder of the Notes, promptly after the Expiration Date. All
Notes represented by Certificates delivered to the Exchange Agent will be deemed
to have been tendered unless otherwise indicated.

      Except as otherwise provided herein, tenders of Notes may be withdrawn at
any time on or prior to 5:00 p.m., New York City time, on the Expiration Date.
In order for a withdrawal to be effective on or prior to that time, a written,
telegraphic, telex or facsimile transmission of such notice of withdrawal must
be timely received by the Exchange Agent at one of its addresses set forth above
or in the Prospectus on or prior to 5:00 p.m., New York City time, on the
Expiration Date. Any such notice of withdrawal must specify the name of the
person who tendered the Notes to be withdrawn, the aggregate principal amount of
Notes to be withdrawn, and (if Certificates of Notes have been tendered) the
name of the registered holder of the Notes as set forth on the Certificate for
the Notes; if different from that of the person who tendered such Notes. If
Certificates for the Notes have been delivered or otherwise identified to the
Exchange


                                       13
<PAGE>   14
Agent, then prior to the physical release of such Certificates for the Notes,
the tendering holder must submit the serial numbers shown on the particular
Certificates for the Notes to be withdrawn and the signature on the notice of
withdrawal must be guaranteed by an Eligible Institution, except in the case of
Notes tendered for the account of an Eligible Institution. If Notes have been
tendered pursuant to the procedures for book-entry transfer set forth in the
Prospectus under "The Registered Exchange Offer -- Registered Exchange Offer
Procedures," the notice of withdrawal must specify the name and number of the
account at DTC to be credited with the withdrawal of Notes, in which case a
notice of withdrawal will be effective if delivered to the Exchange Agent by
written, telegraphic, telex or facsimile transmission. Withdrawals of tenders of
Notes may not be rescinded. Notes properly withdrawn will not be deemed validly
tendered for purposes of the Exchange Offer, but may be retendered at any
subsequent time on or prior to 5:00 p.m., New York City time, on the Expiration
Date by following any of the procedures described in the Prospectus under "The
Registered Exchange Offer -- Registered Exchange Offer Procedures."

      All questions as to the validity, form and eligibility (including time of
receipt) of such withdrawal notices will be determined by Giant, in its sole
discretion, which determination shall be final and binding on all parties. None
of Giant, any affiliates or assigns of Giant, the Exchange Agent or any other
person shall be under any duty to give any notification of any irregularities in
any notice of withdrawal or incur any liability for failure to give any such
notification. Any Notes which have been tendered but which are withdrawn will be
returned to the holder thereof without cost to such holder promptly after
withdrawal.

      5. SIGNATURES ON LETTER OF TRANSMITTAL, ASSIGNMENTS AND ENDORSEMENTS. If
this Letter of Transmittal is signed by the registered holder(s) of the Notes
tendered hereby, the signature(s) must correspond exactly with the name(s) as
written on the face of the Certificate(s) without alteration, enlargement or any
change whatsoever.

      If any of the Notes tendered are owned of record by two or more joint
owners, all such owners must sign this Letter of Transmittal.

      If any tendered Notes are registered in different name(s) on several
Certificates, it will be necessary to complete, sign and submit as many separate
Letters of Transmittal (or facsimiles thereof) as there are different
registrations of Certificates.

      If this Letter of Transmittal or any Certificates or bond powers are
signed by trustees, executors, administrators, guardians, attorneys-in-fact,
officers of corporations or others acting in a fiduciary or representative
capacity, such persons should so indicate when signing and must submit proper
evidence satisfactory to Giant, in its sole discretion, of each such person's
authority so to act.

      When this Letter of Transmittal is signed by the registered owner(s) of
the Notes listed and transmitted hereby, no endorsement(s) of Certificate(s) or
separate bond power(s) are required unless Notes are to be issued in the name of
a person other than the registered holder(s). Signature(s) on such
Certificate(s) or bond power(s) must be guaranteed by an Eligible Institution.


                                       14
<PAGE>   15
      If this Letter of Transmittal is signed by a person other than the
registered owner(s) of the Notes listed, the Certificates must be endorsed or
accompanied by appropriate bond powers, signed exactly as the name or names of
the registered owner(s) appear(s) on the Certificates, and also must be
accompanied by such opinions of counsel, certifications and other information as
Giant may require in accordance with the restrictions on transfer applicable to
the Notes. Signatures on such Certificates or bond powers must be guaranteed by
an Eligible Institution.

      6. SPECIAL ISSUANCE AND DELIVERY INSTRUCTIONS. If Notes are to be issued
in the name of a person other than the signer of this Letter of Transmittal, or
if Notes are to be sent to someone other than the signer of this Letter of
Transmittal or to an address other than that shown above, the appropriate boxes
on this Letter of Transmittal should be completed. Certificates for Notes not
exchanged will be returned by mail or, if tendered by book-entry transfer, by
crediting the account indicated above maintained at DTC. See Instruction 4.

      7. Giant will determine, in its sole discretion, all questions as to the
form of documents, validity, eligibility (including time of receipt) and
acceptance for exchange of any tender of Notes, which determination shall be
final and binding on all parties. Giant reserves the absolute right to reject
any and all tenders determined by it not to be in proper form or the acceptance
of which, or exchange for which, may, in the view of counsel to Giant, be
unlawful. Giant also reserves the absolute right, subject to applicable law, to
waive any of the conditions of the Exchange Offer set forth in the Prospectus
under "The Registered Exchange Offer -- Conditions" or any conditions or
irregularity in any tender of Notes of any particular holder whether or not
similar conditions or irregularities are waived in the case of other holders.
Giant's interpretation of the terms and conditions of the Exchange Offer
(including this Letter of Transmittal and the instructions hereto) will be final
and binding. No tender of Notes will be deemed to have been validly made until
all irregularities with respect to such tender have been cured or waived. Giant,
any affiliates or assigns of Giant, the Exchange Agent, or any other person
shall not be under any duty to give notification of any irregularities in
tenders or incur any liability for failure to give such notification.

      8. QUESTIONS, REQUESTS FOR ASSISTANCE AND ADDITIONAL COPIES. Questions and
requests for assistance may be directed to the Exchange Agent at its address and
telephone number set forth on the front of this Letter of Transmittal.
Additional copies of the Prospectus, the Notice of Guaranteed Delivery and the
Letter of Transmittal may be obtained from the Exchange Agent or from your
broker, dealer, commercial bank, trust company or other nominee.

      9. 31% BACKUP WITHHOLDING; SUBSTITUTE FORM W-9. Under U.S. Federal income
tax law, a holder whose tendered Notes are accepted for exchange is required to
provide the Exchange Agent with such holder's correct taxpayer identification
number ("TIN") on Substitute Form W-9 below. If the Exchange Agent is not
provided with the Correct TIN, the Internal Revenue Service (the "IRS") may
subject the holder or other payee to a $50 penalty. In addition, payments to
such holders or other payees with respect to Notes exchanged pursuant to the
Exchange Offer may be subject to 31% backup withholding.

      The box in Part 2 of the Substitute Form W-9 may be checked if the
tendering holder has not been issued a TIN and has applied for a TIN or intends
to apply for a TIN in the near future. If the box in Part 2 is checked, the
holder or other payee must also complete the Certificate of


                                       15
<PAGE>   16
Awaiting Taxpayer Identification Number below in order to avoid backup
withholding. Notwithstanding that the box in Part 2 is checked and the
Certificate of Awaiting Taxpayer Identification Number is completed, the
Exchange Agent will withhold 31% of all payments made prior to the time a
properly certified TIN is provided to the Exchange Agent. The Exchange Agent
will retain such amounts withheld during the 60-day period following the date of
the Substitute Form W-9. If the holder furnishes the Exchange Agent with its TIN
within 60 days after the date of the Substitute Form W-9, the amounts retained
during the 60-day period will be remitted to the holder and no further amounts
shall be retained or withheld from payments made to the holder thereafter. If,
however, the holder has not provided the Exchange Agent with its TIN within such
60-day period, amounts withheld will be remitted to the IRS as backup
withholding. In addition, 31% of all payments made thereafter will be withheld
and remitted to the IRS until a correct TIN is provided.

      The holder is required to give the Exchange Agent the TIN (e.g., social
security number or employer identification number) of the registered owner of
the Notes or of the last transferee appearing on the transfers attached to, or
endorsed on, the Notes. If the Notes are registered in more than one name or are
not in the name of the actual owner, consult the enclosed "Guidelines for
Certification of Taxpayer Identification Number on Substitute Form W-9" for
additional guidance on which number to report.

      Certain holders (including, among others, corporations, financial
institutions and certain foreign persons) may not be subject to these backup
withholding and reporting requirements. Such holders should nevertheless
complete the attached Substitute Form W-9 below, and write "exempt" on the face
thereof, to avoid possible erroneous backup withholding. A foreign person may
qualify as an exempt recipient by submitting a properly completed IRS Form W-8,
signed under penalties of perjury, attesting to that holder's exempt status.
Please consult the enclosed "Guidelines for Certification of Taxpayer
Identification Number on Substitute Form W-9" for additional guidance on which
holders are exempt from backup withholding.

      Backup withholding is not an additional U.S. Federal income tax. Rather,
the U.S. Federal income tax liability of a person subject to backup withholding
will be reduced by the amount of tax withheld. If withholding results in an
overpayment of taxes, a refund may be obtained.

      10. WAIVER OF CONDITIONS. The Company reserves the absolute right to waive
satisfaction of any or all conditions enumerated in the Prospectus.

      11. NO CONDITIONAL TENDERS. No alternative, conditional, irregular or
contingent tenders will be accepted. All tendering holders of Notes, by
execution of this Letter of Transmittal, shall waive any right to receive notice
of the acceptance of their Notes for exchanges.

      Neither the Company, the Exchange Agent nor any other person is obligated
to give notice of any defect or irregularity with respect to any tender of Notes
nor shall any of them incur any liability for failure to give any such notice.


                                       16
<PAGE>   17
      12. LOST, DESTROYED OR STOLEN CERTIFICATES. If any Certificate(s)
representing Notes have been lost, destroyed or stolen, the holder should
promptly notify the Exchange Agent. The holder will then be instructed as to the
steps that must be taken in order to replace the Certificate(s). This Letter of
Transmittal and related documents cannot be processed until the procedures for
replacing lost, destroyed or stolen Certificate(s) have been followed.

      13. SECURITY TRANSFER TAXES. Holders who tender their Notes for exchange
will not be obligated to pay any transfer taxes in connection therewith. If,
however, Exchange Notes are to be delivered to, or are to be issued in the name
of, any person other than the registered holder of the Notes tendered, or if a
transfer tax is imposed for any reason other than the exchange of Notes in
connection with the Exchange Offer, then the amount of any such transfer tax
(whether imposed on the registered holder or any other persons) will be payable
by the tendering holder. If satisfactory evidence of payment of such taxes or
exemption therefrom is not submitted with the Letter of Transmittal, the amount
of such transfer taxes will be billed directly to such tendering holder.

      IMPORTANT: THIS LETTER OF TRANSMITTAL (OR FACSIMILE THEREOF) AND ALL OTHER
REQUIRED DOCUMENTS MUST BE RECEIVED BY THE EXCHANGE AGENT ON OR PRIOR TO 5:00
P.M., NEW YORK CITY TIME, ON THE EXPIRATION DATE.


                                       17
<PAGE>   18
TO BE COMPLETED BY ALL TENDERING SECURITYHOLDERS
                             (See Instruction 9)

                      PAYER'S NAME: THE BANK OF NEW YORK

--------------------------------------------------------------------------------
SUBSTITUTE

Form W-9 Department Of The Treasury Internal Revenue Service

Payor's Request For Taxpayer Identification Number ("TIN") and Certification
--------------------------------------------------------------------------------
PART 1 - PLEASE PROVIDE YOUR TIN ON THE LINE AT RIGHT AND CERTIFY BY SIGNING AND
DATING BELOW
--------------------------------------------------------------------------------
PART 2 - TIN Applied For  / /
--------------------------------------------------------------------------------
CERTIFICATION - UNDER THE PENALTIES OF PERJURY, I CERTIFY THAT:

(1)   the number shown on this form is my correct taxpayer identification number
      (or I am waiting for a number to be issued to me).


(2)   I am not subject to backup withholding either because (i) I am exempt from
      backup withholding, (ii) I have not been notified by the Internal Revenue
      Service ("IRS") that I am subject to backup withholding as a result of a
      failure to report all interest or dividends, or (iii) the IRS has notified
      me that I am no longer subject to backup withholding, and

(3)   any other information provided on this form is true and correct.


 Signature _____________________________    Date ________________, 1997


--------------------------------------------------------------------------------

TIN:__________________________ Social Security Number or Employer Identification
Number

--------------------------------------------------------------------------------
You must cross out item (iii) in Part (2) above if you have been notified by the
IRS that you are subject to backup withholding because of underreporting
interest or dividends on your tax return and you have not been notified by the
IRS that you are no longer subject to backup withholding.
--------------------------------------------------------------------------------

NOTE: FAILURE TO COMPLETE AND RETURN THIS FORM MAY IN CERTAIN CIRCUMSTANCES
RESULT IN BACKUP WITHHOLDING OF 31% OF ANY AMOUNTS PAID TO YOU PURSUANT TO THE
EXCHANGE OFFER. PLEASE REVIEW THE ENCLOSED GUIDELINES FOR CERTIFICATION OF
TAXPAYER IDENTIFICATION NUMBER ON SUBSTITUTE FORM W-9 FOR ADDITIONAL DETAILS.

      YOU MUST COMPLETE THE FOLLOWING CERTIFICATE IF YOU CHECKED THE BOX
                       IN PART 2 OF SUBSTITUTE FORM W-9

--------------------------------------------------------------------------------
            CERTIFICATE OF AWAITING TAXPAYER IDENTIFICATION NUMBER

I certify under penalties of perjury that a taxpayer identification number has
not been issued to me, and either (1) I have mailed or delivered an application
to receive a taxpayer identification number to the appropriate Internal Revenue
Service Center or Social Security Administration Office or (2) I intend to mail
or deliver an application in the near future. I understand that if I do not
provide a taxpayer identification number by the time of payment, 31% of all
payments made to me on account of the Exchange Notes shall be retained until I
provide a taxpayer identification number to the Exchange Agent and that, if I do
not provide my taxpayer identification number within 60 days, such retained
amounts shall be remitted to the Internal Revenue Service as backup withholding
and 31% of all reportable payments made to me thereafter will be withheld and
remitted to the Internal Revenue Service until I provide a taxpayer
identification number.

Signature ________________________________     Date ______________________,1997

--------------------------------------------------------------------------------


                                       18