Exhibit 24

                                POWER OF ATTORNEY

        KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes and
appoints each of Michael S. Frankel, Adeel Khan, Dan Elisha, Cher Riban and
Marie Ly, signing singly, with full power of substitution, as the undersigned's
true and lawful attorney-in-fact to:

        (1)     prepare, execute in the undersigned's name and on the
undersigned's behalf, and submit to the U.S. Securities and Exchange Commission
(the "SEC") a Form ID, including amendments thereto, and any other documents
necessary or appropriate to obtain codes and passwords enabling the undersigned
to make electronic filings with the SEC of reports required by Section 16(a) of
the Securities Exchange Act of 1934 or any rule or regulation of the SEC;

        (2)     execute for and on behalf of the undersigned, in the
undersigned's capacity as an officer and/or director of Rexford Industrial, Inc.
(the "Company") and/or 10% holder of the Company's capital stock, Forms 3, 4,
and 5 and any amendments thereto in accordance with Section 16(a) of the
Securities Exchange Act of 1934 and the rules thereunder;

        (3)     do and perform any and all acts for and on behalf of the
undersigned which may be necessary or desirable to complete and execute any such
Form 3, 4, or 5, complete and execute any amendment or amendments thereto, and
timely file such form with the SEC and any stock exchange or similar authority;
and

        (4)     take any other action of any type whatsoever in connection with
the foregoing which, in the opinion of such attorney-in-fact, may be of benefit
to, in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in such
attorney-in-fact's discretion.

        The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this power of attorney and the
rights and powers herein granted. The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the
undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 18th day of July, 2013.

                             Signature: /s/ Howard Schwimmer
                                        ---------------------------------------
                             Name:      Howard Schwimmer