According to the Fresnel diffraction theory, a simulation model of grating-based X-ray differential phase contrast imaging system was established. A PMMA sphere was the image object and the level of X-ray was 30 keV. Through the simulation, the change of the wave front of the X-ray passing through the sphere and phase grating was gotten. In addition, the image of first-order derivative of object phase was extracted by the method of phase-stepping. Furthermore, the influence of Moire fringe contrast on image quality was analyzed. The optimization design of the parameters of the grating was discussed. The simulation results are helpful to optimize the experimental platform, and analyze the factors that affecting the image quality.