<PAGE>
 
                                                                    EXHIBIT 10.5

                                                            June 25, 1998



 
Mr. Jon F. Vein
c/o Patti Felker, Esq.
Nelson, Guggenheim, Felker & Levine
10880 Wilshire Blvd., Suite 2070
Los Angeles, CA 90024

Dear Mr. Vein:

     Please refer to that certain agreement between you (therein and herein
"Executive") and us (therein and herein "Company") dated as of the first day of
August 1997 (the "Agreement").

     For good and valuable consideration, the Agreement is amended and modified
as follows:

     1.  Effective immediately, in lieu of services described in paragraph 1.2
of the Agreement, Executive shall serve as Executive Vice President performing
(i) services overseeing feature development and production, (ii) services as
supervisor of the business affairs and internal legal areas, and (iii) services
involved in exploring and developing areas of activity in which the Company
might be involved, i.e. new development,  and  (iv) any other duties including
all activities incidental thereto which are consistent with Executive's title as
may be assigned to him by the Company's Chief Executive Officer or the Board of
Directors.

     2.   The Initial Term of the Agreement will be deemed to expire as of
August 2, 1998;  the Term of the Agreement shall be and hereby is extended for a
period of two (2) additional contract years (as defined as the Agreement)
commencing August 3, 1998 and continuing through August 2, 2000 (which period
consists of the "second contract year" and the "third contract year"
respectively).

     3.  The base salary for the second contract year and the third contract
year shall be as follows:

     (i)   second contract year  $235,000.00
 
     (ii)  third contract year    $250,000.00

all payable in weekly or bi-weekly installments as Company elects.
<PAGE>
 
     4.  If Company's Board of Directors hereafter determines to establish a
bonus plan for senior executives, then Executive shall be entitled to
participate in said plan, as one of the senior executives, upon such terms as
may be determined by the Board of Directors, based upon recommendations of its
Compensation Committee and the Chief Executive Officer of Company.

     5.  With respect to paragraph to 6.2(a), it is agreed that in addition to
the shares of Film Roman, Inc., a Delaware corporation ("Delaware Company") as
to which Executive currently has options, i.e., 62,500 shares, Company shall
cause the Delaware Company to grant to Executive the right and option to
purchase from the Delaware Company all or any part of an aggregate of 50,000
additional shares upon the same terms and conditions as are set forth in the
Stock Option Agreement currently in force between the Delaware Company and
Executive.  The purchase price of such additional shares shall be the fair
market value thereof (as defined in the Stock Option Plan) as of June 16, 1998.

     Additionally, in response to an offer from the Delaware Company, Executive
has elected to cancel his existing stock options and exchange the same for
options to purchase 62,500 shares of the common stock of the Delaware Company at
a purchase price equal to the fair market value of such shares as of June 16,
1998.  In this regard it is understood that the existing options and the options
granted hereunder shall vest, in the aggregate, as follows:

<TABLE> 
<CAPTION> 
                      OPTIONS SHALL BECOME EXERCISABLE
                      WITH RESPECT TO THE FOLLOWING
     ON OR AFTER      CUMULATIVE NUMBER OF SHARES
     -----------      ---------------------------
<S>                    <C>  
September 1, 1998          20%, i.e. 20,500 shares
September 1, 1999          20%, i.e. 20,500 shares
September 1, 2000          20%, i.e. 20,500 shares
September 1, 2001          20%, i.e. 20,500 shares
September 1, 2002          20%, i.e. 20,500 shares
</TABLE> 

     No term or condition of the Agreement is amended or modified except as
herein expressly set forth and the Agreement as so modified shall be and hereby
is mutually confirmed and ratified.
<PAGE>
 
     Please indicate your agreement with the foregoing by signing in the space
provided below.

                                       Very truly yours,

                                       FILM ROMAN, INC.


                                       By:    /s/ David Pritchard
                                           --------------------------------


AGREED AND ACCEPTED



/s/ Jon F. Vein
-------------------------------
JON F. VEIN