X-ray phase-contrast computed tomography (CT) is based on the difference in phase contrast of the materials during imaging by X-ray to describe the density or thickness of the materials. The use of phase contrast is suitable for weak-absorption materials and to diminish the total absorption dose, enhancing the conditions of the entire imaging procedure and decreasing the damage to the materials. In this paper, we introduce and compared three methods used for X-ray phase-contrast computed tomography, the experiments and the process of image reconstruction.