A curved hologram can increase the view angle in a holographic display. The huge data processing and curved computer-generated hologram (CCGH) computation time is still a challenge for real-time display. Here, we propose two fast methods to accelerate the computation. The first one is a diffraction compensation (DC) method where the diffraction calculation is from the wave-front recording plane (WRP) to a CCGH. The other is an approximate compensation (AC) method that adds a phase difference distribution to the WRP to obtain the CCGH. Numerical simulations and optical experiments are performed, which demonstrate that the two methods are feasible and the computation time is dramatically reduced. The AC method can further reduce time significantly compared with the DC method. And the image quality for proposed methods is similar. It is expected that these fast methods can be combined with curved display screen and flexible display materials in the future.