Fresnel incoherent correlation holography (FINCH) realizes non-scanning three-dimension (3D) images using spatial incoherent illumination, but it requires phase-shifting technology to remove the disturbance of the DC term and twin term that appears in the reconstruction field, thus increasing the complexity of the experiment and limits the real-time performance of FINCH. Here, we propose a single-shot Fresnel incoherent correlation holography via deep learning based phase-shifting (FINCH/DLPS) method to realize rapid and high-precision image reconstruction using only a collected interferogram. A phase-shifting network is designed to implement the phase-shifting operation of FINCH. The trained network can conveniently predict two interferograms with the phase shift of 2/3 π and 4/3 π from one input interferogram. Using the conventional three-step phase-shifting algorithm, we can conveniently remove the DC term and twin term of the FINCH reconstruction and obtain high-precision reconstruction through the back propagation algorithm. The Mixed National Institute of Standards and Technology (MNIST) dataset is used to verify the feasibility of the proposed method through experiments. In the test with the MNIST dataset, the reconstruction results demonstrate that in addition to high-precision reconstruction, the proposed FINCH/DLPS method also can effectively retain the 3D information by calibrating the back propagation distance in the case of reducing the complexity of the experiment, further indicating the feasibility and superiority of the proposed FINCH/DLPS method.