Curved Computer-Generated Hologram (CCGH) can increase the Field of View (FOV) in holographic display. However, the huge data processing is still a challenge for real-time display. A fast calculation method for CCGH based on double-step Fresnel Diffraction (DSF) is proposed. The method includes two steps: the first step is to use DSF to generate a planar computer-generated hologram, and the second step is to compensate the planar computer-generated hologram into a curved computer-generated hologram according to the law of light diffraction propagation. Numerical simulation results show that compared with the direct calculation using the point source method, the calculation time is greatly shortened, and the quality of the reconstructed image meets the viewing needs of the human eye. The optical experiment results are consistent with the numerical simulation results. It is expected that the proposed method can be widely used in real-time curved holographic display in the future.