Phase-contrast computed tomography (CT), different from traditional absorption-contrast tomography, is a novel X-ray inspection method and has been widely used for it′s high sensitivity, high resolution and better reconstructions for soft tissues. However, phase-contrat CT usually leads to unacceptably long exposure time and huge X-ray doses. Sparse angular algorithms show significant advantage over in reducing the X-ray doses. Thus, the study of sparse angular differential phase-contrast CT (DPC-CT) is particularly meaningful. After analyzing the characteristics of the DPC-CT, the Bregman operator splitting (BOS) algorithm is introduced into DPC-CT reconstruction and an alternating iteration algorithm for sparse angular DPC-CT is proposed. The numerical simulation and experiment results show that the proposed algorithm can obtain higher reconstruction quality in sparse angular condition.