A computer generated holographic stereogram based on the wavefront recording plane (WRP) is presented. A WRP closed to the parallax image plane is introduced to record the complex amplitude in a small region for each point in the parallax image. By using three times of fast Fourier transform (FFT) to execute the Fresnel diffraction calculation between the WRP and the holographic stereogram plane, the object wave contributing to the hologram pattern can be achieved. The computation complexity of the proposed approach is dramatically reduced. The results show that the calculation time can be decreased by more than one order of magnitude.