We report a reconstruction method, called a back-projection filtered (BPF) algorithm, for fan beam differential phase contrast computed tomography (DPC-CT) with equidistant geometrical configuration. This work comprises a numerical study of the algorithm and its experimental verification with a three-grating interferometer and an x-ray tube source. The numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated datasets. It could be of interest in future medical phase contrast imaging applications.