The self-diffusion of a single Re adatom on the Re clusters with 967–8263 atoms is studied. The minimum-energy diffusion paths and the corresponding energy barriers for adatom diffusion on the Re hexahedral structure clusters surfaces are determined through a combination of the quenched molecular dynamics (MD) and nudged elastic bands (NEB) methods. Within the studied cluster size range, the ES barriers for an adatom across the step from a (0001) facet to a neighboring () facet are the same. This means that the ES barriers are independent of the size of the clusters, while, the ES barriers for an adatom across the step between two () facet have some dependence on the number of the shell (k). The ES barriers of the clusters with k = even number is lower than that of the clusters with k = odd number. For the former, the ES barriers decrease with increasing cluster size.