Using molecular dynamics simulations based on the embedded atom method, we present the calculations of adsorption and activation energies for the diffusion of adatoms (Cu, Ag or Au) on Cu (100), Ag (100) or Au (100) surfaces with steps. We have also examined the relaxation trends and bond lengths of the adatoms for both fourfold and bridge sites. We note that the vertical distance of the adatom relaxation to the first nearest neighbors is the largest (1.56 %) for Ag on Cu (100) and the shortest (–14.58 %) for Cu on Au (100) as compared to other systems. On the other hand, for Cu on the Au (100) system, we find the adatom barrier for hopping along the step edges to be 0.44 eV, which is the highest for this process among the systems studied here, but the lowest barrier is found for Ag on Cu (100) compared to other systems and costs only 0.20 eV. Attention has also been focused on the evaluations of the adsorption and activation energies for the nine systems in the presence of step edges. The diffusion barriers over and along step edges are interpreted in terms of the cohesive energies of the adatoms and substrates. Moreover, these results can offer some basic rules for forecasting precise atomic surface morphologies in homo- and hetero-epitaxial growth.