<PAGE>   1
                                                                    EXHIBIT 10.6



                                ESCROW AGREEMENT

         THIS ESCROW AGREEMENT, dated as of March _____, 2000 ("Escrow
Agreement"), is by and among BARGO ENERGY COMPANY, a Texas corporation
("Issuer"); the persons listed on Exhibit A hereto (each an "Equity Investor"
and collectively the "Equity Investors"); CHASE BANK OF TEXAS, NATIONAL
ASSOCIATION, as administrative agent (in such capacity, the "Administrative
Agent") for each of the lenders (the "Lenders") now or hereafter party to the
hereinafter defined Credit Agreement; and CHASE BANK OF TEXAS, NATIONAL
ASSOCIATION, acting for the benefit of the Issuer, each Equity Investor and the
Administrative Agent (acting in such capacity, the "Escrow Agent").

                                   BACKGROUND

         A. Issuer, Equity Investors and Administrative Agent have entered into
that certain Assignment, Acknowledgment, Agreement and Waiver dated as of March
_____, 2000 (the "Underlying Agreement") whereby, pursuant to the terms thereof,
Issuer, Equity Investors and Administrative Agent agreed to enter into this
Escrow Agreement with the Escrow Agent.

         B. In order to establish the escrow of the Escrow Items (hereinafter
defined) and to effect the provisions of the Underlying Agreement, the parties
hereto have entered into this Escrow Agreement.

                             STATEMENT OF AGREEMENT

         NOW THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, for
themselves, their successors and assigns, hereby agree as follows:

               1. DEFINITIONS. The following terms shall have the following
meanings when used herein:

                  COMMON STOCK means the common stock, $0.01 par value, of the
Issuer.

                  ESCROW ITEMS shall mean the Preferred Stock Certificates, the
Warrants, the Transfer Agent Instructions, the Purchase Notice, and the Purchase
Price deposited with Escrow Agent pursuant to this Escrow Agreement, together
with any interest and other income thereon.

                  PREFERRED STOCK means the Cumulative Redeemable Preferred
Stock, Series C, of the Issuer, $0.01 par value per share.



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                  PREFERRED STOCK CERTIFICATES means certificates representing
shares of Preferred Stock one registered in the name of each Equity Investor,
duly executed on behalf of the Issuer, with the number of shares represented by
such certificates left blank.

                  PURCHASE NOTICE means notices executed by the Issuer under the
Subscription Agreement accepting the subscription of the Equity Investors to
purchase shares of Preferred Stock, Common Stock or Warrants to purchase Common
Stock.

                  SUBSCRIPTION AGREEMENT shall mean the Subscription Agreement
dated as of March _____, 2000, between the Issuer and each Equity Investor,
relating to the purchase of shares of Preferred Stock and, at the election of
the Equity Investor, Common Stock or Warrants by such Equity Investor from the
Issuer, and any and all amendments, supplements, modifications, additions,
renewals and/or restatements thereof.

                  SUBSCRIPTION FUNDS shall mean the purchase price of Preferred
Stock and Common Stock or Warrants paid by each Equity Investor pursuant to the
Subscription Agreement.

                  TRANSFER AGENT INSTRUCTIONS means a letter addressed to the
transfer agent for the Common Stock of the Issuer instructing the transfer agent
to issue certificates representing shares of Common Stock to each Equity
Investor pursuant to the Subscription Agreement, and setting forth the number of
shares of Common Stock issued to each Equity Investor.

                  WARRANT AGREEMENT means the warrant agreement to purchase
shares of Common Stock of the Issuer one issued in the name of each Equity
Investor, duly executed on behalf of the Issuer, with the number of shares of
common stock issuable upon exercise of the warrants left blank.

                  WARRANTS means warrants, exercisable for ten years, to
purchase shares of Common Stock of the Issuer for $0.01 per share.

               2. APPOINTMENT OF AND ACCEPTANCE BY ESCROW AGENT. Issuer, each
Equity Investor and Administrative Agent hereby appoint Escrow Agent to serve as
escrow agent hereunder. Escrow Agent hereby accepts such appointment and, upon
deposit of the Escrow Items in accordance with Section 3 below, agrees to hold
and disburse the Escrow Items in accordance with this Escrow Agreement.

               3. DEPOSITS INTO ESCROW OF ESCROW ITEMS.

                  (a)      Issuer has delivered the Preferred Stock
                           Certificates, the Warrant Agreements and the Transfer
                           Agent Instructions to the Escrow Agent to be held on
                           behalf of the Issuer.

                  (b)      Following receipt of the Purchase Notice from the
                           Administrative Agent (in accordance with the
                           Subscription Agreement) and provided (i) the
                           Expiration Date did not occur prior to such delivery
                           and (ii) the conditions

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                           precedent to the Equity Investor's obligations set
                           forth in Section 4.5 of the Subscription Notice have
                           been satisfied, each Equity Investor will deposit its
                           Subscription Funds with the Escrow Agent to the
                           following account on or before the Closing Date (as
                           defined in the Subscription Agreement):

                           Chase Bank of Texas, National Association
                           ABA# _________________
                           Account#________________
                           ATTN: ______________________________
                           Re: Bargo Energy Company

               4. DISBURSEMENTS FROM ESCROW. The funds and documents
deposited into Escrow pursuant hereto shall be distributed as follows:

                  (a) Upon receipt, prior to the Expiration Date (as defined in
         the Subscription Agreement), of a certificate executed by an officer of
         the Administrative Agent stating that the Tranche A Equity Subscription
         Date has occurred and that amounts remain outstanding on the Tranche A
         Loan, the Escrow Agent shall deliver the Purchase Notices to the
         Administrative Agent. The Escrow Agent shall send copies of such
         Purchase Notices and the Administrative Agent's certificate delivered
         under this subsection (a) to the Issuer.

                  (b) Upon receipt of Subscription Funds from an Equity Investor
         and a certificate executed by an officer of the Administrative Agent
         which states the number of shares of Preferred Stock and Common Stock
         or Warrants that the Equity Investor has purchased from the Issuer, the
         Escrow Agent shall (i) deliver by wire transfer to the Administrative
         Agent the amount of the Subscription Funds, (ii) complete the Preferred
         Stock Certificate by filling in the number of shares of Preferred Stock
         purchased by the Equity Investor (as indicated in the Administrative
         Agent's certificate) and deliver to such Equity Investor the Preferred
         Stock Certificate, (iii) if the Administrative Agent's certificate
         states that the Equity Investor has purchased Common Stock, complete
         the Transfer Agent Instructions by filling in the number of shares of
         Common Stock purchased (as indicated in such the Administrative Agent's
         certificate) and send to the transfer agent the Transfer Agent
         Instructions instructing the transfer agent to issue certificates to
         the Equity Investor representing shares of Common Stock and (iii) if
         the Administrative Agent's certificate states that the Equity Investor
         has purchased Warrants, complete the Warrant by filling in the number
         of shares of Common Stock subject to the Warrants (as indicated in the
         Administrative Agent's certificate) and send the Warrants to the Equity
         Investor. The Escrow Agent shall send copies of the Preferred Stock
         Certificates, Transfer Agent Instructions or Warrants sent to each
         Equity Investor, as well as a copy of the Administrative Agent's
         certificate delivered under this subsection (b) to the Issuer.

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                  (c) Upon receipt of a certificate executed by an officer of
         the Administrative Agent stating that (a) the Tranche A Term Loan has
         been paid in full or (b) the Expiration Date (as defined in the
         Subscription Agreement) has occurred prior to Purchase Notices being
         delivered to the Equity Investors, the Escrow Agent shall deliver all
         Escrowed Items not previously distributed from Escrow to the Issuer.

      5. SUSPENSION OF PERFORMANCE; DISBURSEMENT INTO COURT. If, at any time,
there shall exist any dispute between Issuer, any Equity Investor or the
Administrative Agent with respect to the holding or disposition of any portion
of the Escrow Items or any other obligations of Escrow Agent hereunder, or if at
any time Escrow Agent is unable to determine, to Escrow Agent's sole
satisfaction, the proper disposition of any portion of the Escrow Items or
Escrow Agent's proper actions with respect to its obligations hereunder, or if
the Administrative Agent has not within 30 days of the furnishing by Escrow
Agent of a notice of resignation pursuant to Section 6 hereof, appointed a
successor Escrow Agent to act hereunder, then Escrow Agent may, in its sole
discretion, take either or both of the following actions:

                  a. suspend the performance of any of its obligations
(including without limitation any disbursement obligations) under this Escrow
Agreement until such dispute or uncertainty shall be resolved to the sole
satisfaction of Escrow Agent or until a successor Escrow Agent shall have been
appointed (as the case may be).

                  b. petition (by means of an interpleader action or any other
appropriate method) any court of competent jurisdiction in any venue convenient
to Escrow Agent, for instructions with respect to such dispute or uncertainty,
and to the extent required by law, pay into such court, for holding and
disposition in accordance with the instructions of such court, all Escrow Items
held by it, after deduction and payment to Escrow Agent of all fees and expenses
(including court costs and attorneys' fees) payable to, incurred by, or expected
to be incurred by Escrow Agent in connection with the performance of its duties
and the exercise of its rights hereunder.

         Escrow Agent shall have no liability to Issuer, any Equity Investor,
Administrative Agent or any other person with respect to any such suspension of
performance or disbursement into court, specifically including any liability or
claimed liability that may arise, or be alleged to have arisen, out of or as a
result of any delay in the disbursement of the Escrow Items held by it or any
delay in or with respect to any other action required or requested of Escrow
Agent.

      6. RESIGNATION AND REMOVAL OF ESCROW AGENT. Escrow Agent may resign
from the performance of its duties hereunder at any time by giving ten (10)
days' prior written notice to the Administrative Agent or may be removed, with
or without cause, by Issuer, Equity Investors and Administrative Agent, acting
jointly, at any time by the giving of ten (10) days' prior written notice to
Escrow Agent. Such resignation or removal shall take effect upon the appointment
of a successor Escrow Agent as provided hereinbelow. Upon any such notice of
resignation or removal, the Issuer, Equity Investors and Administrative Agent,
acting jointly, shall appoint a successor Escrow Agent hereunder, which shall be
a commercial bank, trust company or other

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financial institution with a combined capital and surplus in excess of
$10,000,000. Upon the acceptance in writing of any appointment as Escrow Agent
hereunder by a successor Escrow Agent, such successor Escrow Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Escrow Agent, and the retiring Escrow Agent shall be
discharged from its duties and obligations under this Escrow Agreement, but
shall not be discharged from any liability for actions taken as Escrow Agent
hereunder prior to such succession. After any retiring Escrow Agent's
resignation or removal, the provisions of this Escrow Agreement shall inure to
its benefit as to any actions taken or omitted to be taken by it while it was
Escrow Agent under this Escrow Agreement. The retiring Escrow Agent shall
transmit all records pertaining to the Escrow Items and shall deliver all Escrow
Items held by it to the successor Escrow Agent, after making copies of such
records as the retiring Escrow Agent deems advisable and after deduction and
payment to the retiring Escrow Agent of all fees and expenses (including court
costs and attorneys' fees) payable to, incurred by, or expected to be incurred
by the retiring Escrow Agent in connection with the performance of its duties
and the exercise of its rights hereunder.

               7. LIABILITY OF ESCROW AGENT.

                  a. Escrow Agent shall have no liability or obligation with
respect to the Escrow Items except for Escrow Agent's willful misconduct or
gross negligence. Escrow Agent's sole responsibility shall be for the
safekeeping, and disbursement of the Escrow Items in accordance with the terms
of this Escrow Agreement. Escrow Agent shall have no implied duties or
obligations and shall not be charged with knowledge or notice of any fact or
circumstance not specifically set forth herein. Escrow Agent may rely upon any
instrument, not only as to its due execution, validity and effectiveness, but
also as to the truth and accuracy of any information contained therein, which
Escrow Agent shall in good faith believe to be genuine, to have been signed or
presented by the person or parties purporting to sign the same and to conform to
the provisions of this Escrow Agreement. In no event shall Escrow Agent be
liable for incidental, indirect, special, consequential or punitive damages.
Escrow Agent shall not be obligated to take any legal action or commence any
proceeding in connection with the Escrow Items, any account in which Escrow
Items are deposited, this Escrow Agreement or the Underlying Agreement, or to
appear in, prosecute or defend any such legal action or proceeding. Escrow Agent
may consult legal counsel selected by it in the event of any dispute or question
as to the construction of any of the provisions hereof or of any other agreement
or of its duties hereunder, or relating to any dispute involving any party
hereto, and shall incur no liability and shall be fully indemnified from any
liability whatsoever in acting in accordance with the opinion or instruction of
such counsel. Issuer and Equity Investors, jointly and severally, shall promptly
pay, upon demand, the reasonable fees and expenses of any such counsel.

         b. The Escrow Agent is authorized, in its sole discretion, to comply
with orders issued or process entered by any court with respect to the Escrow
Items, without determination by the Escrow Agent of such court's jurisdiction in
the matter. If any portion of the Escrow Items is at any time attached,
garnished or levied upon under any court order, or in case the payment,
assignment, transfer, conveyance or delivery of any such property shall be
stayed or

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enjoined by any court order, or in case any order, judgment or decree shall be
made or entered by any court affecting such property or any part thereof, then
and in any such event, the Escrow Agent is authorized, in its sole discretion,
to rely upon and comply with any such order, writ, judgment or decree which it
is advised by legal counsel selected by it is binding upon it without the need
for appeal or other action; and if the Escrow Agent complies with any such
order, writ, judgment or decree, it shall not be liable to any of the parties
hereto or to any other person or entity by reason of such compliance even though
such order, writ, judgment or decree may be subsequently reversed, modified,
annulled, set aside or vacated.

               8. INDEMNIFICATION OF ESCROW AGENT. From and at all times
after the date of this Escrow Agreement, Issuer and Equity Investors, jointly
and severally, shall, to the fullest extent permitted by law and to the extent
provided herein, indemnify and hold harmless Escrow Agent and each director (in
his or her capacity as a director of Escrow Agent), officer, employee, attorney,
agent and affiliate of Escrow Agent (collectively, the "Indemnified Parties")
against any and all actions, claims (whether or not valid), losses, damages,
liabilities, costs and expenses of any kind or nature whatsoever (including
without limitation reasonable attorneys' fees, costs and expenses) incurred by
or asserted against any of the Indemnified Parties from and after the date
hereof, whether direct, indirect or consequential, as a result of or arising
from or in any way relating to any claim, demand, suit, action or proceeding
(including any inquiry or investigation) by any person, including without
limitation Issuer or any Equity Investor, whether threatened or initiated,
asserting a claim for any legal or equitable remedy against any person under any
statute or regulation, including, but not limited to, any federal or state
securities laws, or under any common law or equitable cause or otherwise,
arising from or in connection with the negotiation, preparation, execution,
performance or failure of performance of this Escrow Agreement or any
transactions contemplated herein, whether or not any such Indemnified Party is a
party to any such action, proceeding, suit or the target of any such inquiry or
investigation; provided, however, that no Indemnified Party shall have the right
to be indemnified hereunder for any liability finally determined by a court of
competent jurisdiction, subject to no further appeal, to have resulted solely
from the gross negligence or willful misconduct of such Indemnified Party. If
any such action or claim shall be brought or asserted against any Indemnified
Party, such Indemnified Party shall promptly notify Issuer and Equity Investors
in writing, and Issuer and Equity Investors shall assume the defense thereof,
including the employment of counsel and the payment of all expenses. Such
Indemnified Party shall, in its sole discretion, have the right to employ
separate counsel (who may be selected by such Indemnified Party in its sole
discretion) in any such action and to participate in the defense thereof, and
the fees and expenses of such counsel shall be paid by such Indemnified Party,
except that Issuer and Equity Investors shall be required to pay such fees and
expenses if (a) Issuer and/or Equity Investors agree to pay such fees and
expenses, or (b) Issuer and/or Equity Investors shall fail to assume the defense
of such action or proceeding or shall fail, in the sole discretion of such
Indemnified Party, to employ counsel satisfactory to the Indemnified Party in
any such action or proceeding, (c) Issuer and/or Equity Investors is the
plaintiff in any such action or proceeding or (d) the named or potential parties
to any such action or proceeding (including any potentially impleaded parties)
include both Indemnified Party and Issuer and/or Equity Investors, and
Indemnified Party shall have been advised by counsel that there may be one or
more legal defenses available to it which are

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different from or additional to those available to Issuer and/or Equity
Investors. Issuer and/or Equity Investors shall be jointly and severally liable
to pay fees and expenses of counsel pursuant to the preceding sentence, except
that any obligation to pay under clause (a) shall apply only to the party so
agreeing. All such fees and expenses payable by Issuer and/or Equity Investors
pursuant to the foregoing sentence shall be paid from time to time as incurred,
both in advance of and after the final disposition of such action or claim. All
of the foregoing losses, damages, costs and expenses of the Indemnified Parties
shall be payable by Issuer and/or Equity Investors, jointly and severally, to
the extent of the Escrow Items upon demand by such Indemnified Party. Upon
exhaustion of the Escrow Items, the indemnification obligations of Issuer and
Equity Investors hereunder shall be borne by Issuer and Equity Investors,
jointly and severally. The obligations of Issuer and Equity Investors under this
Section 8 shall survive any termination of this Escrow Agreement, and the
resignation or removal of Escrow Agent shall be independent of any obligation of
the Escrow Agent.

         The parties agree that neither the payment by Issuer or Equity
Investors of any claim by Escrow Agent for indemnification hereunder nor the
disbursement of any amounts to Escrow Agent from the Escrow Items in respect of
a claim by Escrow Agent for indemnification shall impair, limit, modify or
affect, as between Issuer and Equity Investors, the respective rights and
obligations of Issuer, on the one hand, and Equity Investors, on the other hand,
under the Underlying Agreement.

         9. FEES AND EXPENSES OF ESCROW AGENT. None.

         10. NOTICE. All notices required to be given hereunder shall be in
writing, shall be given by telecopier, with original to follow, and shall be
deemed given when received by telecopier at the address for notices specified
under the parties signatures on the signature pages hereof until such time as
the parties hereto designate a different or additional address or addresses.

         11. AMENDMENT OR WAIVER. This Escrow Agreement may be changed, waived,
discharged or terminated only by a writing signed by the Issuer, Equity
Investors, Administrative Agent and Escrow Agent. No delay or omission by any
party in exercising any right with respect hereto shall operate as a waiver. A
waiver on any one occasion shall not be construed as a bar to, or waiver of, any
right or remedy on any future occasion.

         12. SEVERABILITY. To the extent any provision of this Escrow Agreement
is prohibited by or invalid under applicable law, such provision shall be
ineffective to the extent of such prohibition or invalidity, without
invalidating the remainder of such provision or the remaining provisions of this
Escrow Agreement.

         13. GOVERNING LAW. This Escrow Agreement shall be construed and
interpreted in accordance with the internal laws of the State of Texas.

         14. ENTIRE AGREEMENT. This Escrow Agreement [and the Underlying
Agreement] constitute(s) the entire agreement between the parties relating to
the holding and disbursement of

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the Escrow Items and sets forth in their entirety the obligations and duties of
Escrow Agent with respect to the Escrow Items.

         15. BINDING EFFECT. All of the terms of this Escrow Agreement, as
amended from time to time, shall be binding upon, inure to the benefit of and be
enforceable by the respective heirs, successors and assigns of Issuer, Equity
Investors, Administrative Agent and Escrow Agent.

         16. EXECUTION IN COUNTERPARTS. This Escrow Agreement may be executed in
two or more counterparts, which when so executed shall constitute one and the
same agreement or direction. This Escrow Agreement and any document in
connection herewith may be sent by facsimile transmission, which when so sent
shall be deemed an original executed document delivered for all purposes hereof.

         17. TERMINATION. Upon the first to occur of the disbursement of all
Escrow Items or the disbursement of all Escrow Items into court pursuant to
Section 5 hereof, this Escrow Agreement shall terminate and Escrow Agent shall
have no further obligation or liability whatsoever with respect to this Escrow
Agreement or the Escrow Items.



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         IN WITNESS WHEREOF, the parties hereto have caused this Escrow
Agreement to be executed under seal as of the date first above written.


                    ISSUER:

                    BARGO ENERGY COMPANY


                    By:
                       ---------------------------------
                    Name:
                         -------------------------------
                    Title:
                          ------------------------------


                    Address for Notices:


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

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

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


                    ENERGY CAPITAL INVESTMENT CO., PLC



                    By:
                       -------------------------------------------
                       Gary R. Petersen
                       Director

                    ENCAP ENERGY CAPITAL FUND III, L.P.
                    By: EnCap Investments L.L.C., General Partner



                    By:
                       -------------------------------------------
                       D. Martin Phillips
                       Managing Director

                    ENCAP ENERGY CAPITAL FUND III-B L.P.
                    By: EnCap Investments L.L.C., General Partner



                    By:
                       -------------------------------------------
                       D. Martin Phillips
                       Managing Director


<PAGE>   10



ENCAP EQUITY 1994, L.P.
By: EnCap Investments L.L.C., General Partner


By:
   -------------------------------------------
   D. Martin Phillips
   Managing Director


BOCP PARTNERS, L.P.
By: EnCap Investments L.L.C., Manager



By:
   -------------------------------------------
   D. Martin Phillips
   Managing Director

EOS PARTNERS, L.P.
By: Eos SBIC General, L.P., its general partner
    By: Eos SBIC, Inc., its general partner



By:
   -------------------------------------------
   Brian D. Young
   General Partner

EOS PARTNERS SBIC, L.P.
By: Eos SBIC General, L.P., its general partner
    By: Eos SBIC, Inc., its general partner



By:
   -------------------------------------------
   Brian D. Young
   President



<PAGE>   11


EOS PARTNERS SBIC II, L.P.
By: Eos SBIC General II, L.P., its general partner
    By: Eos SBIC II, Inc., its general partner



By:
   -------------------------------------------
   Brian D. Young
   President

SGC PARTNERS II LLC



By:
   -------------------------------------------
   V. Frank Pottow
   Managing Director

BANCAMERICA CAPITAL INVESTORS SBIC I, L.P.
By: BancAmerica Capital Management SBIC I, LLC, its general partner
    By: BancAmerica Capital Management I, L.P., its sole member
        By: BACM I GP, LLC, its general partner



By:
   -------------------------------------------
   J. Travis Hain
   Managing Director

KAYNE ANDERSON ENERGY L.P.
By: Kayne Anderson Capital Advisors, L.P., its General Partner
    By: Kayne Anderson Investment Management, Inc., its General Partner



By:
   -------------------------------------------
   Daniel M. Weingeist
   Managing Director



<PAGE>   12


ADMINISTRATIVE AGENT:


CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
as Administrative Agent


By:
   ---------------------------------
Name:
     -------------------------------
Title:
      ------------------------------


Address for Notices:


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

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

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


ESCROW AGENT:


CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
as Escrow Agent


By:
   ---------------------------------
Name:
     -------------------------------
Title:
      ------------------------------


Address for Notices:


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

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