POWER OF ATTORNEY

        Know all by these presents, that the undersigned hereby constitutes and
appoints William D. Young with full power of substitution, 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, as amended (the
                "Exchange Act") or any rule or regulation of the SEC;

        (2)     execute for and on behalf of the undersigned, in the
                undersigned's capacity as a beneficial owner of more than 10% of
                the capital stock of Continental Building Products, Inc. (the
                "Company"), Forms 3, 4, and 5 in accordance with Section 16(a)
                of the Exchange Act and the rules thereunder and Schedules 13D
                and 13G in accordance with Section 13 of the Exchange Act 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 or Schedules 13D or 13G,
                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 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 attorney-in-fact, in
serving in such capacity at the request of the undersigned, is not assuming, nor
is the Company assuming, any of the undersigned's responsibilities to comply
with Sections 13 and 16 of the Exchange Act.

        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 attorney-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 16th day of March 2016.

                                        /s/ John P. Grayken
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                                        Signature

                                        John P. Grayken
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