Using empirical embedded atom method (EAM) potential, activation barriers of adatom diffusion on the surface, diffusion along the step edge, and island corner diffusion are calculated for metal (111) surface (Pt, Ag) and the behavior of those barriers is investigated with respect to lattice strain. Based on the calculated barriers, we perform the kinetic Monte Carlo simulation for monolayer island growth and for how the variation of the activation barriers with lattice strain changes the island growth. Results from this work show that the lattice strain transforms the island growth shape from $$\left\langle {\bar 1\bar 12} \right\rangle $$ dendritic through random fractal to $$\left\langle {11\bar 2} \right\rangle $$ denditic at 100 K and from triangular through hexagonal to inverse triangular at 400 K.