LIMITED POWER OF ATTORNEY

                                      FOR

                           CONE Midstream Partners LP

                             SECTION 16(a) FILINGS

                                October 23, 2017

Know all by these presents, that the undersigned hereby constitutes and appoints
Kirk A. Moore signing singly, the undersigned's true and lawful attorney-in-fact
to:

     1.  execute for and on behalf of the undersigned, in the undersigned's
         capacity as an officer or director of the general partner of CONE
         Midstream Partners LP (the "Partnership"), Forms 3, 4 and 5 and
         amendments thereto in accordance with Section 16(a) of the Securities
         Exchange Act of 1934, as amended, and the rules promulgated thereunder;

     2.  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 amendment thereto and timely file such form with the
         United States Securities and Exchange Commission (the "SEC") and any
         stock exchange or similar authority; and

     3.  take any other action of any type whatsoever 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
         document executed by such attorney-in-fact on behalf of the undersigned
         pursuant to this Limited Power of Attorney shall be in such form and
         shall contain such terms and conditions as such attorney-in-fact may
         approve.

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 Limited 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, one not assuming,
nor is the Partnership assuming, any of the undersigned's responsibilities to
comply with Section 16 of the Securities Exchange Act of 1934.

This Limited 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 transaction in securities of the Partnership,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact. This Limited Power of Attorney may be filed with the
SEC as a confirming statement of the authority granted herein.

IN WITNESS WHEREOF, the undersigned has caused this Limited Power of Attorney to
be executed as of the date first written above.

                                           /s/ Raymond T. Betler
                                           ------------------------------------
                                                  Raymond T. Betler