A vector theory for diffraction of multi step phase grating is presented. The half numerical method converts differential equation into generalized eigenvalue equation. At matching the boundary conditions in the longitudinal direction, a mode conversion matrix is introduced together with the reflection and transmission coefficient matrices. The iteration formula of the amplitude coefficient of the electric field are derived out. Finally the diffraction efficiency for each order of the transmission wave and the reflection wave are obtained in the any polarization.The computer program developed from the method has much less amount of calculation so that it can work on PC fast and stable. The method presented in this paper provides a simple fast algorithm to design binary optical element by vector diffraction. The results show that the scalar theory results differ greatly with that of the vector theory in the certain condition.