AMENDMENT NO. 1 to CONSULTING AGREEMENT datedMay 3, 2012 by and between AXIS Specialty Limited (the Company) and Michael A. Butt (theConsultant) Dated December 5, 2013

Exhibit 10.4

AMENDMENT NO. 1

to

CONSULTING AGREEMENT

dated May 3, 2012

by and between

AXIS Specialty Limited (the “Company”)

and

Michael A. Butt (the “Consultant”)

Dated December 5, 2013

WHEREAS, the Company and the Consultant entered into a consulting agreement dated as of May 3, 2012 (the “Agreement”); and

WHEREAS, the Compensation Committee of the Board of Directors of AXIS Capital Holdings Limited, the Company and the Consultant have determined that it is in the best interests of the Company and its shareholders to make certain revisions to the Agreement in order to extend the term of service thereof;

NOW, THEREFORE, the Agreement is hereby amended, effective as of the date hereof, as follows:

“3. Consulting Fee. During the Consulting Term, in consideration of the services to be provided by the Consultant to the Company described herein and in consideration for the covenants of the Consultant set forth herein, the Company shall pay the Consultant a fee in the amount of $950,000, payable in the amount of $237,500 no later than the first business day of January, April, July and October 2014. The Company will pay all applicable Bermuda payroll taxes attributable to Consultant’s services during the Consulting Term. The Consultant shall not be entitled to participate in any employee benefit plans maintained by the Company or any of its Affiliates by reason of this Agreement.”

[signatures on following page]

IN WITNESS WHEREOF, the undersigned have executed this Amendment as of the date first written above.