Reported here is the first observation of the tunneling surface diffusion of a hydrogen (H) atom on water ice. Photostimulated desorption and resonance-enhanced multiphoton ionization methods were used to determine the diffusion rates at 10 Kon amorphous solid water and polycrystalline ice. H-atom diffusion on polycrystalline ice was 2 orders of magnitude faster than that of deuterium atoms, indicating the occurrence of tunneling diffusion. Whether diffusion is by tunneling or thermal hopping also depends on the diffusion length of the atoms and the morphology of the surface. Our findings contribute to a better understanding of elementary physicochemical processes of hydrogen on cosmic ice dust.