n a three-dimensional display by a computer-generated hologram (CGH), fast computation of CGH is required. In this paper, in order to accelerate CGH generation, the following two methods are used; the first method is band-limited double-step Fresnel diffraction. Compared with convolution-based diffraction, such as an angular spectral method, the proposed method requires less computational time and memory. The second method is a wavefront recording plane (WRP) method which reduces the calculation amount by placing WRPs in the vicinity of an object. We succeeded in speeding up CGH calculation by combining both methods.