Monte-Carlo master equation (MCME) method has been proposed to simulate the structural evolution of epitaxial growth system in relatively large scale (10(3)-10(6) atoms). It enables us to describe the structural evolution of epitaxial growth in both single-element and binary system. Probabilities, such as adsorption, scattering. desorption, atomic-site jump(diffusion), are taken into account in the manner of master equation. which describe a local reaction energetics of growing surface atoms. Growth simulations of three types of conditions: equilibrium, super-cooling and super-saturation, have been made for Si humoepitaxy on Si(001). The results showed the clear difference in the features of growth rate and roughness among these conditions.