Diffractive optical element (DOE) which maintains beam shape and intensity distribution precisely with high efficiency of the source is used as the beam shaping and smoothing element for the off-axis illumination (OAI) of lithographic system. A vector analyzing model of DOE for lithography is established based on vector angular-spectrum method, and the performance of DOE designed by using scalar algorithm such as uniformity and beam shaping is analyzed. The results show that the scalar approximation cannot fit the requirement when the diffraction angle of DOE is large and the dimension of DOE is reduced to the working wavelength, or large error of caculations will be caused.