Cross sections and rate constants are presented for the rotational excitation of OH in collision with ortho and para-H-2, using a new ab initio interaction potential [Offer and Van Hemert, J. Chem. Phys. 99, 3836 (1993)]. The cross sections are given at a number of energies and are compared with those calculated using an earlier potential energy surface, and with the available experimental results. A strong oscillatory behavior is found in the cross sections for collisions with ground state para-H-2 which was not apparent in earlier calculations. The oscillatory behavior is very much reduced in collisions with ortho-H-2. Rate constants obtained by averaging the cross sections over a Maxwell-Boltzmann velocity distribution are given at a temperature of 300 K. Expressions for calculating the hyperfine resolved cross sections by transforming the S-matrices are discussed for the case where H-2 is no longer constrained to its rotational ground state, and cross sections for transitions between the hyperfine resolved levels are given for collisions with both para and ortho-H-2.