Differential phase contrast computerized tomography (DPC-CT) is a novel X-ray inspection method. However, DPC-CT usually requires several sampling attempts, which will inevitablly introduce unacceptabe long exposure time and huge X-ray doses. Sparse angular algorithms show significant advantage in reducing the exposure time and X-ray doses. Thus, the study of sparse angular DPC-CT is particularly important. After analyzing the characteristics of the DPC-CT, we introduce the compressive sensing theory into the DPC-CT reconstruction and propose a reconstruction algorithm for DPC-CT named as ART-L1 algorithm which fuse the L1 constraint into the ART algorithm. The numerical simulation and experimental results show that the ART-L1 algorithm can significantly improve the image quality of the sparse angular DPC-CT reconstructions.