We propose, in this paper, a theoretical model to investigate surface self-diffusion of single adatoms on the face-centered-cubic metals. Calculations are performed on both close packed (111) and loosely packed (001) planes of rhodium and nickel. Two realistic model potentials are applied to describe the interatomic interaction of the adatom/substrate systems. The first model is a Morse-type potential, which involves several empirical fitting of bulk properties of solid. The second newly popular potential was introduced by Sutton and Chen, which incorporates with many-body effects. With these potentials, conventional molecular dynamics (MD) is employed to obtain trajectories of the atoms. The averaged square displacements are computed for a range of initial kinetic energies, and the surface diffusion constants can be obtained by means of the Einstein relation. The estimated random walk exponential prefactors and activation energies exhibit Arrhenius behavior, which are confirmed with the previous results. Surface migration by an exchange mechanism for self-diffusion on the Ni(001) plane is also discussed.