The diffusion dynamics of hydrogen in bulk and nanocrystalline palladium has been examined using quasielastic neutron scattering (QENS). With respect to bulk PdH0.73, two relaxation processes were found. For both processes, the variation of the relaxation times with momentum transfer was well reproduced by a model of jump diffusion between adjacent octahedral sites. Upon cooling the fast relaxation fraction decreases. The result suggests that the slow relaxation corresponds to jumps between the ground states and the fast one between excited states. In nanocrystalline PdH0.47 with a size of 8 nm, we found a new fast diffusion process with a smaller activation energy in addition to the one observed in the bulk sample. The new process could be due to the motion of hydrogen atoms in the subsurface region where the potential energy surface is substantially modified by surface strain/distortion effects. This is the first QENS experiment that probes hydrogen diffusion within Pd nanoparticles.