X-ray differential phase contrast imaging technology can reveal the weakly absorbing fine structure which cannot be observed by the conventional X-ray absorption contrast imaging. Hence, it has potential applications in many fields such as medical science, and material science. But in the traditional X-ray grating differential phase contrast imaging system, the analyser grating is used as a spatial filter, and needs to be phase stepped, then multiple exposures are required for information extraction. Thus this leads to high-dose radiation exposure and low efficiency of X-ray utilization. All these disadvantages limit its application in various disciplines. In order to cope with the above issues, a new algorithm based on single-shot grating differential phase contrast imaging system without analyzer grating is proposed. In such a system the absorption, refraction and scattering information can be obtained from one projective image of the sample acquired by a high-resolution detector. The reliability of this new algorithm is confirmed by numerical simulation. Compared with the phase stepping algorithm, the proposed algorithm can provide very accurate and reliable information extraction results without requiring the grating period to match with detector pixel size. It facilitates the reduction of the radiation damage to sample. We emphasize that this method is highly compatible with the future X-ray phase contrast imaging clinical applications.