An accurate full-dimensional global potential energy surface (PES) is developed for the title reaction. The PES was based on similar to 30 000 points at the Davidson corrected multireference configuration interaction level with the aug-cc-pVQZ basis set (MRCI+Q/AVQZ). The ab initio points were fitted using the permutation invariant polynomial-neural network (PIP-NN) method with a root-mean-square error of about 3.0 meV or 24 cm(-1). The kinetics of the OH+ + H-2 and OH+ + D-2 reactions were investigated on the PIP-NN PES using a quasi-classical trajectory method and the calculated thermal rate coefficients are in good agreement with the available experimental data. Furthermore, it is predicted based on the PES using the Sudden Vector Projection model that the rotational excitation of OH+ enhances the reaction at low collision energies.