The effects of lattice strain on the step edge diffusion of metal surface (Ag, Pt) are analyzed using molecular statics (MS) based on the semi-empirical embedded atom method (EAM) potential. Based on the calculated barriers, we perform the kinetic Monte Carlo simulation for monolayer island growth. Calculation of the activation barriers of the adatom diffusion on surface, the diffusion over step edge and along step under strained conditions show that the lattice strain has large effects on the energy barriers of various diffusion processes. For example, Ehrlich-Schwoebel (ES) barrier decreases with increase of the lattice strain and diffusions along two different types of steps on (111) surface have a different dependency upon the lattice strain from each other. These different dependencies of the diffusion barrier on the lattice strain give interesting implications on morphological evolution of strained thin film.