Quantum mechanical close coupling calculation of the state-to-state transport and relaxation cross sections have been done for Hg-H2 molecular system using a high-level ab initio potential energy surface. Rotationally averaged cross sections were also calculated to obtain the energy dependent Senftleben-Beenakker cross sections at the energy range of 0.005–25,000cm−1. Boltzmann averaging of the energy dependent Senftleben-Beenakker cross sections showed the temperature dependency over a wide temperature range of 50–2500K. Interaction viscosity and diffusion coefficients were also calculated using close coupling cross sections and full classical Mason-Monchick approximation. The results were compared with each other and with the available experimental data. It was found that Mason-Monchick approximation for viscosity is more reliable than diffusion coefficient. Furthermore, from the comparison of the experimental diffusion coefficients with the result of the close coupling and Mason-Monchick approximation, it was found that the Hg-H2 potential energy surface used in this work can reliably predict diffusion coefficient data.