AMENDMENT TO REGISTRATION RIGHTS AGREEMENT

Exhibit 10.4

AMENDMENT TO REGISTRATION RIGHTS AGREEMENT

THIS AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (this “Amendment Agreement”), dated as of May 22, 2013, is made by Vantage Driller VI Co. (the “Additional Guarantor”), for the benefit of the Holders of the Notes (including, without limitation, the Initial Purchasers).

All capitalized terms used but not defined herein shall have the meanings assigned in, or incorporated by reference in, the Registration Rights Agreement (as defined below).

W I T N E S S E T H:

WHEREAS, Offshore Group Investment Limited, an exempted company incorporated with limited liability under the laws of the Cayman Islands (the “Company”), entered into that certain Indenture, dated as of March 28, 2013 (as further amended, supplemented, amended and restated or otherwise modified from time to time, the “Indenture”), along with the Guarantors (as defined therein), and Wells Fargo Bank, National Association, as the Trustee and the Noteholder Collateral Agent;

WHEREAS, in connection with the Purchase Agreement, the Company and the Guarantors have entered into that certain Registration Rights Agreement dated as of March 28, 2013 (as amended and in effect, the “Registration Rights Agreement”), in favor of Citigroup Global Markets Inc. and Jefferies LLC, as Representatives of the Initial Purchasers listed in Schedule I to such Registration Rights Agreement for the benefit of the Holders of the Notes (including, without limitation, the Initial Purchasers);

WHEREAS, the Additional Guarantor is executing the Indenture to become a Guarantor, and in connection therewith, the Indenture requires the Additional Guarantor also to become a party to the Registration Rights Agreement in the same way and capacity as the other Guarantors party thereto;

WHEREAS, the requirement that the Additional Guarantor become an additional Guarantor under the Registration Rights Agreement is not a circumstance that would adversely affect any Holder of Registrable Notes; and

WHEREAS, the Additional Guarantor has agreed to execute and deliver this Amendment Agreement in order to become such a party to the Registration Rights Agreement.

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

SECTION 1. Registration Rights Agreement – Agreement to Join. By executing and delivering this Amendment Agreement, the Additional Guarantor hereby joins, and becomes a party to, the Registration Rights Agreement in the same way and capacity as each of the other Guarantors that are parties thereto and for all purposes stated therein as Guarantors, with the same force and effect as if originally named therein as a Guarantor and, without limiting the generality of the foregoing, hereby expressly assumes all obligations and liabilities of a Guarantor thereunder.

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SECTION 2. GOVERNING LAW. THIS AMENDMENT AGREEMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK. THE ADDITIONAL GUARANTOR HEREBY IRREVOCABLY SUBMITS TO THE JURISDICTION OF ANY NEW YORK STATE COURT SITTING IN THE BOROUGH OF MANHATTAN IN THE CITY OF NEW YORK OR ANY FEDERAL COURT SITTING IN THE BOROUGH OF MANHATTAN IN THE CITY OF NEW YORK IN RESPECT OF ANY SUIT, ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT, AND IRREVOCABLY ACCEPTS FOR ITS AND IN RESPECT OF ITS PROPERTY, GENERALLY AND UNCONDITIONALLY, JURISDICTION OF THE AFORESAID COURTS. THE ADDITIONAL GUARANTOR IRREVOCABLY WAIVES, TO THE FULLEST EXTENT IT MAY EFFECTIVELY DO SO UNDER APPLICABLE LAW, TRIAL BY JURY AND ANY OBJECTION THAT IT MAY NOW OR HEREAFTER HAVE TO THE LAYING OF VENUE OF ANY SUCH SUIT, ACTION OR PROCEEDING BROUGHT IN ANY SUCH COURT AND ANY CLAIM THAT ANY SUCH SUIT, ACTION OR PROCEEDING BROUGHT IN ANY SUCH COURT HAS BEEN BROUGHT IN AN INCONVENIENT FORUM. THE ADDITIONAL GUARANTOR IRREVOCABLY CONSENTS, TO THE FULLEST EXTENT IT MAY EFFECTIVELY DO SO UNDER APPLICABLE LAW, TO THE SERVICE OF PROCESS OF ANY OF THE AFOREMENTIONED COURTS IN ANY SUCH ACTION OR PROCEEDING BY THE MAILING OF COPIES THEREOF BY REGISTERED OR CERTIFIED MAIL, POSTAGE PREPAID, TO THE COMPANY AT ITS SAID ADDRESS, SUCH SERVICE TO BECOME EFFECTIVE 30 DAYS AFTER SUCH MAILING. NOTHING HEREIN SHALL AFFECT THE RIGHT OF ANY HOLDER TO SERVE PROCESS IN ANY OTHER MANNER PERMITTED BY LAW OR TO COMMENCE LEGAL PROCEEDINGS OR OTHERWISE PROCEED AGAINST THE ADDITIONAL GUARANTOR IN ANY OTHER JURISDICTION.

SECTION 3. Counterparts. This Amendment Agreement may be executed in one or more counterparts and, if executed in more than one counterpart, the executed counterparts shall each be deemed to be an original but all such counterparts shall together constitute one and the same instrument. It is the express intent of the parties hereto to be bound by the exchange of signatures on this Amendment Agreement via telecopy or other form of electronic transmission.

SECTION 4. Miscellaneous. All terms of the Registration Rights Agreement, except as modified hereby, shall remain in full force and effect.

[Signatures follow in next page]

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IN WITNESS WHEREOF, the undersigned has caused this Amendment Agreement to be duly executed and delivered by it as of the date first above written.

[SIGNATURE PAGE – AMENDMENT AGREEMENT TO REGISTRATION RIGHTS AGREEMENT FOR 2013 NOTES]

[SIGNATURE PAGE – AMENDMENT AGREEMENT TO REGISTRATION RIGHTS AGREEMENT FOR 2013 NOTES]