Exhibit 10.4

FIRST AMENDMENT TO THE GENPACT LIMITED

2007 OMNIBUS INCENTIVE COMPENSATION PLAN

(AS AMENDED AND RESTATED APRIL 11, 2012)

This Amendment (the “Amendment”) to the Genpact Limited 2007 Omnibus Incentive Compensation Plan, as amended and restated April 11, 2012 (the “Plan”) is effective as of August 1, 2012.

WHEREAS, the Plan may be amended by the Board of Directors (the “Board”) of Genpact Limited (the “Company”) in accordance with Section 7 of the Plan; and

WHEREAS, upon the recommendation of the Compensation Committee of the Company, the Board adopted a resolution on August 1, 2012 authorizing this Amendment;

NOW THEREFORE, the Plan is hereby amended as follows:

1. Amendments. The following paragraph is hereby added to the end of the “Change of Control” definition contained in Section 2 of the Plan:

“Notwithstanding the foregoing definition of ‘Change of Control’, (A) the acquisition of Company Voting Securities by South Asia Private Investments (“Investor”), a Mauritus private company limited by shares and an affiliate of Bain Capital LLC (or any of its affiliates or successors) from certain affiliates of General Atlantic LLC and certain affiliates of Oak Hill Capital Management, LLC pursuant to that certain Share Purchase Agreement, dated August 1, 2012 (such acquisition, the “Specified Acquisition”), shall not constitute a Change of Control for purposes of the Plan or any Award Agreement and (B) for purposes of determining whether any acquisition or holdings of voting securities of the Company (including any Company Voting Securities) or any Continuing Entity by Investor (or any of its affiliates or successors) after consummation of the Specified Acquisition would constitute a Change of Control, references to 25% in clause (ii) and clause (iv) of the definition of Change of Control shall, with respect to New Investor, (or any of its affiliates or successors), be deemed to be references to 50%.”

2. Effectiveness. This Amendment will be null and void ab initio and of no further force or effect if the transactions contemplated under that certain Share Purchase Agreement, dated as of August 1, 2012, among Investor and each of the shareholders of the Company listed on Exhibit A and Exhibit B thereto are not consummated.

3. The Plan. Except as specifically amended hereby, all of the terms and other provisions of the Plan are hereby ratified and confirmed and shall continue to be in full force and effect in accordance with their respective terms on the date hereof. Capitalized terms used but not defined in this Amendment shall have the meanings assigned to them in the Plan, except to the extent such terms are modified herein.

4. Headings. The headings contained in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment.

IN WITNESS WHEREOF, the undersigned, a duly authorized officer of the Company, has executed this Amendment as of the date first written above.