Quasi-elastic neutron scattering (QENS) measurements have been performed to investigate the surface selfdiffusion of hydrogen molecules. A monolayer of molecular hydrogen was adsorbed on a carbon material commonly used in polymer electrolyte membrane fuel cells, called XC-72. QENS spectra were recorded at the time-of-flight spectrometer IN5 at Institut Laue-Langevin (ILL) in Grenoble at 40, 50, 60, and 70 K. By using the Chudley & Elliott model for jump diffusion, we found the diffusion coefficient at each temperature. The logarithm of the diffusion coefficient was plotted versus the inverse of the temperature to give the coefficient in the Arrhenius equation. From this, we can estimate the diffusion at higher temperatures as well. Our observed diffusion follows the same trend as that found for hydrogen molecules on the surface of singlewalled carbon nanotubes and Grafoil.