Viewing angle of the conventional flat hologram is not very large (less than 180°) attributed to their planar observation surface. If we want to synthesize a wide view computer generated hologram, a numerical simulation of the diffraction on the non-planar observation surfaces is required, computer generated cylindrical hologram (CGCH) can be a solution. Approximately 2,500 object points were used for this research. We have realized a CGCH that is viewable in 360°. However, the heavy computation load is one of the issues. Therefore, we propose a fast calculation method for a computer generated cylindrical hologram by the use of wave-front recording surface. The wave-front recording surface is placed between the object data and a CGCH. When the wave-front recording surface is placed close to the object, the object light passes through a small region on the wave recording surface. Therefore the computational complexity for the object light is very small. We can obtain a CGCH to execute diffraction calculation from the wave-front recording surface, propagating the recorded optical field of the wave-front recording surface to the cylindrical hologram surface using only two FFT operations and hence is much faster.