The adatom diffusion barriers on homoepitaxial three-dimensional (3D) Cu(111) islands with different numbers of monolayers have been studied by using molecular dynamics simulation combined with a molecular statics method. The parameter of atomic interaction potentials, which has been introduced in the embedded atom method, was applied in the simulation. The influence of 3D islands with different numbers of monolayers on the hopping diffusion and the exchange diffusion has been discussed in the paper. The results show that the two-dimensional (2D) Enrilich-Schwoebel (ES) barriers are lower than the 3D-ES barriers and the 3D-ES barrier is independent of the atomic layers in 3D islands. For the 3D island with (100) side-facet, the adatom diffusion along 〈011〉 will be affected by the number of monolayers in the 3D island. The adatom diffusion on the 3D islands is dominated by downward diffusion mechanism. For the 3D islands with the (111) side-facet, however, upward diffusion on the 3D islands is possible.