Differential phase contrast computed tomography (DPC-CT) is a novel X-ray inspection method which has obvious advantage in detecting weak absorption substance compared with conventional CT reconstruction methods. However, DPC-CT usually need to scan many times in order to obtain enough refraction angle information, which leads to unacceptably long exposure time and huge X-ray doses. Thus, the study of sparse angular DPC-CT reconstruction algorithm is particularly important. After analyzing the characteristics of the DPC-CT. Based on the theoretical framework of projection on convex set (POCS), a reconstruction algorithm for DPC-CT is proposed by combining L1 norm, curvelet coefficient constraint and dassical algebra reconstruction technique (ART). The numerical simulation and experimental results show that the proposed algorithm can significantly improve the image quality of the sparse angular DPC-CT reconstructions.