Collisional data for the excitation of NH by H2 are key to accurately derive the NH abundance in astrophysical media. We present a new four-dimensional potential energy surface (PES) for the NH-H2 van der Waals complex. The ab initio calculations of the PES were carried out using the explicitly correlated partially spin-restricted coupled cluster method with single, double, and perturbative triple excitations [RCCSD(T)-F12a] with the augmented correlation-consistent polarized valence triple zeta basis set. The PES was represented by an angular expansion in terms of coupled spherical harmonics. The global minimum corresponds to the linear structure with a well depth De = 149.10 cm−1. The calculated dissociation energy D0 is found to be 30.55 and 22.11 cm−1 for ortho-H2 and para-H2 complexes, respectively. These results are in agreement with the experimental values. Then, we perform quantum close-coupling calculations of the fine structure resolved excitation cross sections of NH induced by collisions with ortho-H2 and para-H2 for collisional energies up to 500 cm−1. We find strong differences between collisions induced by ortho-H2 and para-H2. Propensity rules are discussed. The cross sections are larger for fine structure conserving transitions than for fine structure changing ones, as predicted by theory. These new results should help in interpreting NH interstellar spectra and better constrain the abundance of NH in interstellar molecular clouds. © 2021 Author(s).