POWER OF ATTORNEY
                                 L. THOMAS STONE

        With respect to holdings of and transactions in securities issued by
PennTex Midstream Partners, LP (the "Company"), the undersigned hereby
constitutes and appoints the individuals named on Schedule A attached hereto and
as may be amended from time to time, or any of them signing singly, with full
power of substitution and resubstitution, to act 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 United States Securities and Exchange
            Commission (the "SEC") a Form ID, including amendments thereto, and
            any other documents necessary or appropriate to obtain and/or
            regenerate 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, or any rule or
            regulation of the SEC;

        2.  execute for and on behalf of the undersigned, Forms 3, 4, and 5 in
            accordance with Section 16 of the Securities Exchange Act of 1934,
            as amended, 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 his or her
            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 and resubstitution or revocation, hereby ratifying and confirming
all that such attorney-in-fact, or such attorneys-in-fact 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 any Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

        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 26th day of May, 2015.

                                        /s/ L. Thomas Stone
                                        ----------------------------------------
                                        L. Thomas Stone

                                   Schedule A

        Individuals Appointed as Attorney-in-Fact with Full Power of
Substitution and Resubstitution

        1.  Steven R. Jones
        2.  Stephen M. Moore