Compared with the semiconductor and micromachining fabrication technology, the holographic lithography method offers a number of advantages, including its ability to create large volume of periodic structures through one irradiation process, the uniformity of period, and more degrees of freedom to control the structures. In this study, a multi-beam interference model is presented for predicting two-and three-dimensional photonic crystal structures through designing the beam intensities, polarization directions and phase delays. Based on plane wave expansion method, complete forbidden bands of three-dimensional photonic crystals with fcc structure are also studied. The calculated results provide a useful guide for choosing proper optical parameters to fabricate two- and three-dimensional photonic crystal structures.