In this paper the epitaxial growth mechanism on vicinal GaAs(001) surface is studied using the kinetic Monte Carlo simulation method. The Ehrlich-Schwoebel barrier has great influence on the growth mechanism of the vicinal surface. The simulation results show that the downward movement to a lower step of the adatoms can be inhibited by Ehrlich-Schwoebel barrier at low temperature, while the adatoms can move to the lower step at high temperature. At the beginning of growth, the adatoms are almost distributed uniformly on the steps. When the surface coverage reaches to certain value, the step nucleation begins. Meanwhile, the adatoms begin to accumulate at the upper step because of the Ehrlich-Schwoebel barrier. If there were no Ehrlich-Schwoebel barrier, the adatoms at the upper step could be depleted completely. The Ehrlich-Schwoebel barrier has great influence on the growth mode of the vicinal surface, and it will increase the temperature for onset of the step growth mode.