<PAGE>
 
                                AMENDMENT NO. 1

                                to that certain

                          SECOND AMENDED AND RESTATED
                          REVOLVING CREDIT AGREEMENT

     This AMENDMENT NO. 1 (this "Amendment"), dated as of December 31, 1998, is
by and among (a) TRICO MARINE OPERATORS, INC. ("Marine Operators"), TRICO MARINE
ASSETS, INC. ("Marine Assets") (each of Marine Operators and Marine Assets is
referred to herein as a "Borrower" and collectively as the "Borrowers"), (b)
TRICO MARINE SERVICES, INC. (the "Parent"), (c) BANKBOSTON, N.A. and the other
lending institutions party to the Credit Agreement referred to below
(collectively, the "Banks"), and (d) BANKBOSTON, N.A. as agent for the Banks
(the "Agent").

     WHEREAS, the Borrowers, the Parent, the Banks and the Agent are parties to
that certain Second Amended and Restated Revolving Credit Agreement, dated as of
March 13, 1998 (as amended, restated, modified or supplemented and in effect
from time to time, the "Credit Agreement"), pursuant to which the Banks and the
Agent upon certain terms and conditions, have agreed to make loans and to
otherwise extend credit to the Borrowers; and

     WHEREAS, the Borrowers and the Parent have requested that the Banks and the
Agent agree to amend certain provisions of the Credit Agreement; and

     WHEREAS, the Banks and the Agent have agreed, subject to the satisfaction
of the conditions precedent set forth herein, to so amend the Credit Agreement;
and

     WHEREAS, capitalized terms which are used herein without definition and
which are defined in the Credit Agreement shall have the same meanings herein as
in the Credit Agreement.

     NOW, THEREFORE, the Borrowers, the Parent, the Banks and the Agent hereby
agree as follows:

     (S)1.  AMENDMENTS TO THE CREDIT AGREEMENT.  Subject to the satisfaction of
the conditions precedent set forth in (S)4 hereof, the Credit Agreement is
hereby amended as follows:
<PAGE>
 
                                       2



          (S)1.1  DEFINITIONS.

          (a) Section 1.1. of the Credit Agreement is hereby amended by deleting
     the definitions of "Applicable Margin" and "Leverage Ratio" set forth
     therein and substituting in lieu thereof the following new definitions:

          Applicable Margin.  (a) With respect to any Base Rate Loan or
     Eurocurrency Rate Loan and for each period commencing on an Adjustment Date
     through the date immediately preceding the next Adjustment Date (each a
     "Rate Adjustment Period"), the Applicable Margin shall be the applicable
     percentage set forth below with respect to the Leverage Ratio, calculated
     on a Pro Forma Basis, if applicable, as of the end of the fiscal quarter of
     the Borrowers immediately preceding the date of the Compliance Certificate
     relating to such Adjustment Date:

<TABLE>
<CAPTION>
                                                       BASE       EUROCURRENCY
 LEVEL                 LEVERAGE RATIO               RATE LOANS     RATE LOANS
 ------                --------------               ----------    ------------ 
<S>        <C>                                      <C>           <C>
I           Greater than 5.00 to 1.00                    0.50%           2.25%
 
 
 
II          Less than or equal to 5.00 to 1.00           0.50%           2.00%
            and greater than 4.00 to 1.00
 
 
 
III         Less than or equal to 4.00 to 1.00           0.50%           1.75%
            and greater than 3.00 to 1.00
 
 
 
IV          Less than or equal to 3.00 to 1.00           0.50%           1.50%
            and greater than 2.50 to 1.00
 
 
 
V           Less than or equal to 2.50 to 1.00           0.25%           1.25%
            and greater than 2.00 to 1.00
 
 
VI          Less than 2.00 to 1.00                       0.25%           1.00%
------------------------------------------------------------------------------
</TABLE>

          (b) If the Borrowers shall fail to deliver any Compliance Certificate
     pursuant to (S)8.4(c) hereof, then, for the period commencing on the date
     such Compliance Certificate was due pursuant to (S)8.4(c) through the
     Adjustment Date immediately following the date on which such Compliance
     Certificate is delivered, the Applicable Margin for each Base Rate Loan or
     Eurocurrency Rate Loan shall be that corresponding to Level I in the table
     above.

          Leverage Ratio.  As at the end of any fiscal quarter, the ratio of (a)
     the consolidated Funded Debt of the Parent and its Subsidiaries at the end
     of the fiscal quarter of the Parent ending on such date to (b) Consolidated
     EBITDA of the Parent and its Subsidiaries for the period of the four (4)
     consecutive fiscal quarters of the Parent ending on such date; provided,
     however, when calculating the Leverage Ratio for any Test Period in which a
     Triggering Acquisition occurred, the calculation of the Leverage Ratio
     shall be made on a Pro Forma Basis.
<PAGE>
 
                                       3

     (b) Section 1.1 of the Credit Agreement is hereby further amended by
inserting the following new definitions therein in the correct alphabetical
sequence:

          Additional SWATH Subsidiary Vessels.  Collectively, the supply boats
     Spirit River and the Hondo River.

          Available Commitment.  $85,000,000; provided that, at any time after
     June 30, 1999, so long as the Leverage Ratio, determined as of the end of
     any fiscal quarter ending after June 30, 1999 and as demonstrated by a
     Compliance Certificate and accompanying financial statements delivered
     pursuant to Section 8.4, is less than 4.0:1.0, the Available Commitment
     shall, commencing on the Adjustment Date corresponding to such Compliance
     Certificate, be increased to an amount equal to $100,000,000.  Thereafter,
     in the event that either (a) the Leverage Ratio as of the end of any fiscal
     quarter is greater than 4.0:1.0 or (b) the Borrowers shall fail to deliver
     a Compliance Certificate and the accompanying financial statements pursuant
     to (S)8.4 hereof, then as at either the Adjustment Date corresponding to
     such Compliance Certificate (if a Compliance Certificate is delivered) or
     the first day of the month in which Compliance Certificate is required by
     Section 8.4 to be delivered (if a Compliance Certificate is not delivered)
     the Available Commitment shall revert to $85,000,000.

          Excluded Capital Expenditures.  For any fiscal year of the Parent,
     collectively, (i) Capital Expenditures not to exceed the amount set forth
     on Schedule 1A hereto incurred by the Borrowers in connection with the
     refurbishment or construction and completion of Vessels, which
     refurbishment or construction is, as of January 1, 1999, in progress and
     (ii) any Capital Expenditure of the Parent or any of its Subsidiaries,
     where not less than seventy-five percent (75%) of the consideration paid or
     payable by the Parent and its Subsidiaries in connection therewith is
     funded with the proceeds of a Permitted Equity Issuance.

          Maintenance Capital Expenditures.  Capital Expenditures incurred in
     connection with the maintenance, repair, or dry-docking of, and inspection
     costs relating to, Vessels which are owned or are being constructed by the
     Borrowers as of January 1, 1999.

          Permitted Acquisition.  The acquisition by any Person, whether by
     purchase, lease or otherwise, of any Person or specified group of assets;
     provided that such Person is engaged, or such assets are used in, a line of
     business substantially similar to the business now conducted by the Person
     making such acquisition.

          Permitted Equity Issuance.  The issuance by the Parent of common stock
     or convertible preferred stock; provided that the terms of any such
     convertible preferred stock shall be approved in writing by the Agent.

     (c) The definition of "Commitment Fee Rate" set forth in Section 1.1 of the
Credit Agreement is hereby amended by deleting the table set forth in such
definition and substituting in lieu thereof the following new table:
<PAGE>
 
                                       4

<TABLE>
<CAPTION>
 
 LEVEL                       LEVERAGE RATIO                      COMMITMENT FEE
 -----                       --------------                      --------------
<S>        <C>                                                   <C>
I          Greater than 5.00 to 1.00                                       0.50%
 
II         Less than or equal to 5.00 to 1.00 and greater                  0.50%
           than 4.00 to 1.00
 
III        Less than or equal to 4.00 to 1.00 and greater                  0.50%
           than 3.00 to 1.00
 
IV         Less than or equal to 3.00 to 1.00 and greater                 0.375%
           than 2.50 to 1.00
 
V          Less than or equal to 2.50 to 1.00 and greater                 0.375%
           than 2.00 to 1.00
 
VI         Less than 2.00 to 1.00                                          0.25%
-------------------------------------------------------------------------------
</TABLE>

     (d) The definition of "Total Debt Service" set forth in Section 1.1 of the
Credit Agreement is hereby amended by deleting the text "plus (c) Adjusted
Outstandings of such Person for the fiscal quarter of the Borrowers most
recently ended,".

     (S)1.2.   COMMITMENT TO LEND.  Section 2.1 of the Credit Agreement is
hereby amended by deleting the words "Total Commitment" occurring in the twelfth
line thereof and substituting in lieu thereof the words "Available Commitment".

     (S)1.3.   MANDATORY REPAYMENTS OF LOANS.  Section 2.13 of the Credit
Agreement is hereby amended by deleting the words "Total Commitment" occurring
in the third line thereof and substituting in lieu thereof the words "Available
Commitment".

     (S)1.4.   COMMITMENT TO ISSUE LETTERS OF CREDIT.  Section 3.1.1. of the
Credit Agreement is hereby amended by deleting the words "Total Commitment"
occurring in the seventeenth line thereof and substituting in lieu thereof the
words "Available Commitment".

     (S)1.5.   COLLATERAL SECURITY AND GUARANTEES.  The Credit Agreement is
hereby amended by deleting Section 6 thereto in its entirety and substituting in
lieu thereof the following new Section 6:

          (S)6.  COLLATERAL SECURITY AND GUARANTIES.  The Parent and the
     Borrowers covenant and agree as follows:  The Obligations of the Borrowers
     shall be guaranteed equally and ratably by the Parent and each other
     Subsidiary (direct and indirect) of the Parent, to the extent that such
     other Subsidiary of the Parent is required to guaranty the obligations of
     the Parent under the terms of the Indentures relating to the Senior Notes.
<PAGE>
 
                                       5

     The Obligations of the Borrowers shall be secured by a perfected first
     priority security interest (subject only to Permitted Liens entitled to
     priority under applicable law) in (i) certain US Flag Vessels to the extent
     contemplated by the US Vessel Mortgage and (ii) certain other assets of the
     Borrowers to the extent contemplated by the Security Documents.  Promptly
     upon request of the Agent, which may be made from time to time, the
     Borrowers shall grant to the Agent, for the benefit of the Banks and the
     Agent, a perfected first priority security interest in one or more
     Vessel(s) as replacement Collateral hereunder; provided that (i) in
     connection with the grant of any such security interest, the Agent's
     security interest in existing Collateral of equal or greater value shall,
     if such release is permitted pursuant to Section 10.4 hereof, have been
     released by the Agent and (ii) the Borrowers shall not be required to grant
     a security interest as replacement Collateral in any Vessel which is
     subject to a binding purchase agreement with a Person which is not an
     Affiliate of the Borrowers.  The Borrowers shall pay all reasonable costs
     and expenses of the Agent and the Banks and of counsel to the Agent
     incurred in connection with any such replacement of Collateral.

     (S)1.6.   FINANCIAL STATEMENTS, CERTIFICATES AND INFORMATION.  Section 8.4
of the Credit Agreement is hereby amended by deleting paragraph (f) thereof in
its entirety and substituting in lieu thereof the following new paragraph (f):

          (f) once each calendar year, or more frequently as determined by the
     Agent or the Majority Banks, upon the request of the Agent or the Majority
     Banks, the Borrowers will, at their own expense, obtain and deliver to the
     Agent and the Banks appraisal reports in form and substance and from
     appraisers satisfactory to the Agent, stating the then current fair market
     values of the Vessels subject to a Vessel Mortgage; provided, that, (i) the
     Agent may, upon notice to the Borrowers, obtain such appraisals and the
     cost of such appraisals shall be paid by the Borrowers and (ii) unless a
     Default or Event of Default shall have occurred and be continuing, the
     Borrowers shall not be obligated to pay for more than one such appraisal
     which has been obtained or requested by the Agent or the Majority Banks
     during any one calendar year.

     (S)1.7.   INDEBTEDNESS.  (a)  Section 9.1(f) of the Credit Agreement is
hereby amended by adding the words "the Parent," immediately after the words
"more onerous to" occurring in the fifteenth line of such Section.

     (b) Section 9.1(g) of the Credit Agreement is hereby amended by deleting
the proviso set forth in such Section and substituting in lieu thereof the
following new text:  "provided, that (A) the aggregate principal amount of all
such Indebtedness under this clause (g) shall not, at any time, exceed
$50,000,000, (B) the Capital Expenditure or other acquisition associated with
such Indebtedness is permitted pursuant to Section 10.5 or Section 9.5 hereof,
respectively, and (C) after giving effect to the incurrence of any such
Indebtedness, no Default or Event of Default shall have occurred and be
continuing and the Borrowers shall be in compliance with the borrowing
limitations set forth in Section 2.1."

     (c) Section 9.1(k) of the Credit Agreement is hereby further amended by (i)
inserting the number "(i)" immediately before the word "Indebtedness" in such
Section and (ii) inserting the 
<PAGE>
 
                                       6

following new text immediately before the period at the end of such Section:
"and (ii) Indebtedness of the Swath Subsidiary with respect to the Additional
Swath Subsidiary Vessels in an aggregate principal amount not to exceed
$19,000,000; provided that the proceeds of such Indebtedness incurred pursuant
to this clause (ii) shall be used to repay Loans outstanding hereunder".

     (S)1.8.   INVESTMENTS.  Section 9.3 of the Credit Agreement is hereby
amended by deleting paragraphs (e), (f) and (g) thereto in their entirety and
substituting in lieu thereof the following new paragraphs (e), (f), (g), (h),
and (i):

          "(e)  Investments by the Parent or a Borrower in a Borrower;

          (f) Investments (directly or indirectly) by the Parent or the
     Borrowers in a non-Guarantor Subsidiary; provided that the aggregate amount
     of such Investments made during any one fiscal year shall not exceed
     $500,000; and

          (g) (i) Investments by the Parent in the Swath Subsidiary in an
     aggregate amount not to exceed $4,000,000 and (ii) Investments by the
     Parent or the Borrowers in the Swath Subsidiary in an aggregate amount not
     to exceed the lesser of (A) $3,000,000 and (B) the aggregate equity
     investment necessary to be made into the Swath Subsidiary in order to
     complete the financing of the Additional Swath Subsidiary Vessels;

          (h) Investments in acquisitions permitted pursuant to Section 9.5.1.
     hereof; and

          (i) Investments by the Borrowers in the Parent in an aggregate amount
     not to exceed in any one fiscal year of the Borrowers the sum of (i) the
     scheduled payments of principal and interest under the Senior Notes for
     such fiscal year plus (ii) the Borrowers' allocable share of income taxes,
     franchise taxes, professional fees and other operating expenses for such
     year (it being understood that, with respect to the amount of each
     Borrower's allocable share of income taxes, such amount shall not exceed
     the amount of income taxes for which such Borrower would have been liable
     had the accounts of such Borrower not been consolidated with the accounts
     of the Parent) minus (iii) the aggregate amount of Distributions made
     pursuant to Section 9.4 hereof during such fiscal year; provided that no
     Investment (other than Investments the proceeds of which are used to pay
     taxes) shall be made if, after giving effect to such Investment or such
     payment of principal or interest under the Senior Notes, a Default or Event
     of Default shall have occurred and be continuing."

     (S)1.9.   DISTRIBUTIONS.  The Credit Agreement is hereby further amended by
deleting Section 9.4 thereto in its entirety and substituting in lieu thereof
the following new Section 9.4:

          (S)9.4.  DISTRIBUTIONS.   None of the Borrowers nor the Parent will
     make any Distributions other than Distributions by the Borrowers to the
     Parent in an aggregate amount not to exceed in any one fiscal year of the
     Borrowers the sum of (i) the scheduled payments of principal and interest
     under the Senior Notes for such fiscal year plus (ii) the Borrowers'
     allocable share of income taxes, franchise taxes, professional fees and
     other operating 
<PAGE>
 
                                       7

     expenses for such year (it being understood that, with respect to the
     amount of each Borrower's allocable share of income taxes, such amount
     shall not exceed the amount of income taxes for which such Borrower would
     have been liable had the accounts of such Borrower not been consolidated
     with the accounts of the Parent) minus (iii) the aggregate amount of
     Investments made pursuant to Section 9.3(i) hereof during such fiscal year;
     provided that no Distribution (other than Distributions in respect of
     taxes) shall be made if, after giving effect to such Distribution or such
     payment of principal or interest under the Senior Notes, a Default or Event
     of Default shall have occurred and be continuing.

     (S)1.10.  MERGERS AND ACQUISITIONS.  Section 9.5.1. of the Credit Agreement
is hereby amended by (a) inserting the words "(other than a Borrower)"
immediately after the word "Parent" occurring in the fifth line thereof; (b)
deleting the text "or (iii) so long as such merger would not otherwise violate
this Agreement, the merger of one or more other corporations with and into the
Parent, a Borrower or a Subsidiary of the Borrower,"; and (c) deleting the last
sentence of such Section and substituting in lieu thereof the following new
text:

     "The Parent will not, and will not permit any of its Subsidiaries to agree
     to or effect any acquisition of assets or other property, other than (i)
     the acquisition by the Borrowers of Vessels, which are, as of January 1,
     1999, under construction, (ii) acquisitions by the Parent or any of its
     Subsidiaries, where not less than seventy-five percent (75%) of the
     consideration paid or payable by the Parent and its Subsidiaries in
     connection therewith is funded with the proceeds of a Permitted Equity
     Issuance, and (iii) any other Permitted Acquisition by the Parent or any of
     its Subsidiaries, other than the Borrowers, provided that the Capital
     Expenditure associated with such acquisition is permitted pursuant to
     Section 10.5 hereof."

     (S)1.11.  UPSTREAM LIMITATIONS.  Section 9.13 of the Credit Agreement is
hereby amended by deleting clause (iii) thereof in its entirety and substituting
in lieu thereof the text: "(iii) [Intentionally Omitted]".

     (S)1.12.  NO PREPAYMENTS, ETC.  The Credit Agreement is hereby further
amended by adding the following new Section 9.15 thereto in the correct
numerical sequence:

          (S)9.15.  NO PREPAYMENTS, ETC.  The Parent will not, and will not
     permit any of its Subsidiaries to, pay, repay, prepay, redeem, repurchase,
     acquire, retire, defease, or otherwise acquire, all or any portion of the
     Senior Notes in advance of the scheduled maturity date thereof.

     (S)1.13.  DEBT SERVICE COVERAGE RATIO.  The Credit Agreement is hereby
further amended by deleting Section 10.1 thereto in its entirety and
substituting in lieu thereof the following new (S)10.1:

          (S)10.1.  Debt Service Coverage Ratio.  The Parent and the Borrowers
     will not permit the Debt Service Coverage Ratio, determined at the end of
     each fiscal quarter of the Parent ending during a period set forth in the
     table below, to be less than the ratio set forth opposite such period in
     such table:
<PAGE>
 
                                       8

       PERIOD                  RATIO
       ------                  -----   
10/1/98 through 3/31/99       1.50:1.0
4/1/99 through 9/30/99        1.40:1.0
10/1/99 and at all times      1.50:1.0
 thereafter

     (S)1.14. LEVERAGE RATIO. The Credit Agreement is hereby further amended by
deleting (S)10.2 thereto in its entirety and substituting in lieu thereof the
following new (S)10.2:

          (S)10.2.  Leverage Ratio.  The Parent and the Borrowers will not
     permit the Leverage Ratio, determined as at the end of each fiscal quarter
     of the Parent ending during a period set forth in the table below, to be
     greater than the ratio set forth opposite such period in such table:

          PERIOD              LEVERAGE RATIO
          ------              --------------- 
10/1/98 through 12/31/98            4.10:1.0
1/1/99 through 3/31/99              4.80:1.0
4/1/99 through 6/30/99              5.90:1.0
7/1/99 through 9/30/99              6.00:1.0
10/1/99 through 12/31/99            5.90:1.0
1/1/00 through 6/30/00              5.50:1.0
7/1/00 through 12/31/00             4.75:1.0
1/1/01 and at all times             3.50:1.0
 thereafter


     (S)1.15. FUNDED DEBT TO NET WORTH. Section 10.3 of the Credit Agreement is
hereby amended by deleting the ratio "2.0 to 1" set forth in the fourth line
thereof and substituting in lieu thereof the ratio "1.75 to 1".

     (S)1.16.  MINIMUM MORTGAGED VESSEL VALUE.  Section 10.4 of the Credit
Agreement is hereby amended by deleting the percentage "140%" set forth in the
sixth line thereof and substituting in lieu thereof the percentage "175%".

     (S)1.17.  CAPITAL EXPENDITURES.  The Credit Agreement is hereby further
amended by adding the following new Section 10.5 thereto in the correct
numerical location:

          (S)10.5  CAPITAL EXPENDITURES.  The Parent will not, and will not
     permit any of its Subsidiaries to, make Capital Expenditures, other than
     Excluded Capital Expenditures, in an aggregate amount in any fiscal year of
     the Parent in excess of $25,000,000.  In addition, and as a further
     limitation, the Borrowers will not make any Capital Expenditures other than
     (i) Maintenance Capital Expenditures, (ii) Excluded Capital Expenditures,
     and (iii) additional Capital Expenditures; provided that the aggregate
     amount of Capital Expenditures made by the Borrowers during any one fiscal
     year pursuant to this clause (iii) shall not exceed $1,000,000
<PAGE>
 
                                       9

     (S)1.18.  CONDITIONS TO ALL BORROWINGS.  Section 12 of the Credit Agreement
is hereby amended by adding the following new Section 12.5 thereto in the
correct numerical location:

          (S)12.5  OUTSTANDING OBLIGATIONS.  The aggregate amount of Obligations
     outstanding, after giving effect to the making of the Loan and/or the
     issuance of the Letter of Credit requested, shall not exceed the sum of (i)
     $65,000,000 plus (ii) fifteen percent (15%) of Consolidated Net Tangible
     Assets.

     (S)1.19.  CONSENTS, AMENDMENTS, WAIVERS, ETC.  Section 26 of the Credit
Agreement is hereby amended by (i) deleting the following text from such
Section: "the rate of interest on the Notes (other than interest accruing
pursuant to (S)5.8 following the effective date of any waiver by the Majority
Banks of the Default or Event of Default relating thereto),", (ii) deleting the
following text from such Section ", and the rate of the Commitment Fee and the
Letter of Credit Fees", and (iii) adding the following new text immediately
after the word "changed" occurring in the sixteenth line thereof:  ", and the
rate of interest on the Notes (other than interest accruing pursuant to (S)5.8
following the effective date of any waiver by the Majority Banks of the Default
or Event of Default relating thereto) and the amount of Commitment Fee or Letter
of Credit fees hereunder may not be reduced,".

     (S)1.20.  SCHEDULES AND EXHIBITS.  The Credit Agreement is hereby further
amended by (i) deleting Schedule 1.1 thereto and substituting in lieu thereof
Schedule 1.1 attached hereto, (ii) adding Schedule 1A hereto to the Credit
Agreement, and (iii) deleting Exhibit C thereto and substituting in lieu thereof
Exhibit C attached hereto.

     (S)2.  REPRESENTATIONS AND WARRANTIES.  The Parent and each of the
Borrowers jointly and severally represent and warrant to the Banks and the Agent
as follows:

          (a) Representations and Warranties in Credit Agreement.  The
representations and warranties of the Parent and the Borrowers contained in the
Credit Agreement, each as amended by this Amendment, (a) were true and correct
in all material respects when made, and (b) except to the extent such
representations and warranties by their terms are made solely as of a prior
date, continue to be true and correct in all material respects on the date
hereof.

          (b) Authority, Etc.  The execution and delivery by the Borrowers and
the Parent of this Amendment and the performance by the Borrowers and the Parent
of all of their agreements and obligations under this Amendment (i) are within
the corporate authority of each of the Borrowers and the Parent, (ii) have been
duly authorized by all necessary corporate proceedings by each of the Borrowers
and the Parent, (iii) do not conflict with or result in any breach or
contravention of any provision of law, statute, rule or regulation to which
either of the Borrowers or the Parent is subject or any judgment, order, writ,
injunction, license or permit applicable to either of the Borrowers or the
Parent, and (iv) do not conflict with any provision of the corporate charter or
by-laws of, or any agreement or other instrument binding upon, either of the
Borrowers or the Parent.
<PAGE>
 
                                       10

          (c) Enforceability of Obligations.  This Amendment, and the Credit
Agreement as amended hereby, constitute the legal, valid and binding obligations
of each of the Borrowers and the Parent enforceable against each such Person in
accordance with their respective terms.  Immediately prior to and immediately
after and after giving effect to this Amendment, no Default or Event of Default
exists under the Credit Agreement or any other Loan Document.

     (S)3.  AFFIRMATION OF BORROWERS AND THE PARENT.  (a)  Each of the Borrowers
hereby affirms its absolute and unconditional promise to pay to each Bank and
the Agent such Borrower's respective Obligations due under the Notes, the Credit
Agreement as amended hereby, and the other Loan Documents, at the times and in
the amounts provided for therein.  Each of the Borrowers confirms and agrees
that (i) the obligations of the Borrowers to the Banks and the Agent under the
Credit Agreement as amended hereby are secured by and entitled to the benefits
of the Security Documents and (ii) all references to the term "Credit Agreement"
in the Security Documents shall hereafter refer to the Credit Agreement as
amended hereby.

          (b) The Parent hereby acknowledges that it has read and is aware of
the provisions of this Amendment.  The Parent hereby reaffirms its absolute and
unconditional guaranty of the Borrowers' payment and performance of their
obligations to the Banks and the Agent under the Credit Agreement as amended
hereby.  The Parent hereby confirms and agrees that all references in the
Guaranties to the term "Credit Agreement" shall hereafter refer to the Credit
Agreement as amended hereby.

     (S)4.  CONDITIONS TO EFFECTIVENESS.  This Amendment shall be effective as
of the date hereof upon the satisfaction of the following conditions precedent,
on or before January 31, 1999 (each of the following to be in form and substance
satisfactory to the Agent):

          (i) receipt by the Agents of an original counterpart signature to this
     Amendment, duly executed and delivered by the Borrowers, the Parent, the
     Banks and the Agent;

          (ii) each of the Vessels listed on Annex A hereto shall be subject to
     a perfected first priority Vessel Mortgage in favor of the Agent, for the
     benefit of the Banks and the Agent, and the Agent shall have received a
     certificate of ownership or other evidence satisfactory to the Agent of the
     perfection of the Agent's lien on each such Vessel and indicating that
     there shall exist no other liens on any such Vessel;

          (iii)  receipt by the Agent of appropriate corporate authority
     documentation for the Borrowers and the Parent, including copies (to the
     extent not already furnished to the Agent) of each such Person's
     organizational documents, bylaws, if any, and resolutions authorizing the
     transactions contemplated by this Amendment;

          (iv) receipt by the Agents of a legal opinion from counsel to the
     Borrowers and the Parent covering the authorization, execution, delivery
     and enforceability of this Amendment, the Vessel Mortgages referred to in
     (S)4(ii) and the perfection of the Agent's lien in each of the Vessels
     listed on Annex A hereto;
<PAGE>
 
                                       11

          (v) receipt by the Agent, for the pro rata account of each Bank, of an
     amendment fee in an amount for each such Bank equal to one-eighth of one
     percent (0.125%) of such Bank's Total Commitment;

          (vi) the Agent shall have received an appraisal of each of the Vessels
     listed on Annex A hereto;

          (vii)  the Agent shall be satisfied that the fair market value of the
     Vessels which are subject to a first priority perfected Vessel Mortgage in
     favor of the Agent, for the benefit of the Banks and the Agent, is not less
     than $150,000,000;

          (viii)  receipt by the Agent of the amounts payable pursuant to the
     expense letter, dated as of the date hereof, among the Parent, the
     Borrowers, and the Agent; and

          (ix) payment by the Borrowers of all outstanding legal, appraisal, and
     out-of-pocket fees and expenses of the Agent and the Agent's Special
     Counsel.

     (S)5.  MISCELLANEOUS PROVISIONS.  (a)  Except as otherwise expressly
provided by this Amendment, all of the terms, conditions and provisions of the
Credit Agreement shall remain the same.  It is declared and agreed by each of
the parties hereto that the Credit Agreement, as amended hereby, shall continue
in full force and effect, and that this Amendment and the Credit Agreement shall
be read and construed as one instrument.

     (b) THIS AMENDMENT IS INTENDED TO TAKE EFFECT AS AN AGREEMENT UNDER SEAL
AND SHALL BE CONSTRUED ACCORDING TO AND GOVERNED BY THE LAWS OF THE COMMONWEALTH
OF MASSACHUSETTS.

     (c) This Amendment may be executed in any number of counterparts, but all
such counterparts shall together constitute but one instrument.  In making proof
of this Amendment it shall not be necessary to produce or account for more than
one counterpart signed by each party hereto by and against which enforcement
hereof is sought.

     (d) Headings or captions used in this Amendment are for convenience of
reference only and shall not define or limit the provisions hereof.

     (e) The Borrowers hereby jointly and severally agree to pay to the Agent,
on demand by the Agent, all reasonable out-of-pocket costs and expenses incurred
or sustained by the Agent in connection with the preparation of this Amendment
(including collateral appraisal expenses and reasonable legal fees and
expenses).
<PAGE>
 
                                       12


     IN WITNESS WHEREOF, the parties hereto have executed this Amendment as an
agreement under seal as of the date first written above.

                              TRICO MARINE OPERATORS, INC.


                              By:____________________________
                                 Name:
                                 Title:

                              TRICO MARINE ASSETS, INC.


                              By:___________________________
                                  Name:
                                  Title:

                              TRICO MARINE SERVICES, INC.


                              By:___________________________
                                  Name:
                                  Title:


                              BANKBOSTON, N.A., individually and
                                as Agent


                              By:____________________________
                                  Name:
                                  Title:

                              BNY FINANCIAL CORPORATION


                              By:____________________________________
                                  Name:
                                  Title:

                              BANK OF SCOTLAND


                              By:____________________________________
                                  Name:
                                  Title:
<PAGE>
 
                                       13

                              CHRISTIANIA BANK OG KREDITKASSE ASA, NEW YORK
                              BRANCH


                              By:____________________________________
                                  Name:
                                  Title:

                              By:____________________________________
                                  Name:
                                  Title:


                              FIRST UNION NATIONAL BANK (AS SUCCESSOR TO
                              CORESTATES BANK, N.A.)


                              By:____________________________________
                                  Name:
                                  Title:


                              CREDIT LYONNAIS NEW YORK BRANCH


                              By:____________________________________
                                  Name:
                                  Title:


                              BANK ONE, LOUISIANA, NA (AS SUCCESSOR TO FIRST
                              NATIONAL BANK OF COMMERCE)


                              By:____________________________________
                                  Name:
                                  Title:


                              THE FUJI BANK, LIMITED


                              By:____________________________________
                                  Name:
                                  Title:


                              HIBERNIA NATIONAL BANK


                              By:____________________________________
                                  Name:
                                  Title:
<PAGE>
 
                                       14

                              MEESPIERSON CAPITAL CORP.


                              By:____________________________________
                                  Name:
                                  Title:

                              By:____________________________________
                                  Name:
                                  Title:


                              WELLS FARGO BANK (TEXAS) N. A.


                              By:____________________________________
                                  Name:
                                  Title:
<PAGE>
 
                                       15

                                    ANNEX A



VESSEL                        OFFICIAL NUMBER
-------                       ---------------
 
AMITE RIVER                        643782
BIG BLUE RIVER                     646579
BIG HORN RIVER                     616432
BUFFALO RIVER                      610097
ELKHORN RIVER                      603712
FLINT RIVER                        643999
LEIGH RIVER                        583782
MIAMI RIVER                        591621
SOUTHERN RIVER                     588735
STONES RIVER                       649356
SUN RIVER                          627420
TRUCKEE RIVER                      626863
WHITE RIVER                        627699
WOLF RIVER                         653020