A computer-generated hologram based on ray-wavefront conversion can reconstruct photorealistic three-dimensional (3D) images containing deep virtual objects and complicated physical phenomena; however, the required computational cost has been a problem that needs to be solved. In this Letter, we introduce the concept of an orthographic projection in the ray-wavefront conversion technique for reducing the computational cost without degrading the image quality. In the proposed method, plane waves with angular spectra of the object are obtained via orthographic ray sampling and Fourier transformation, and only the plane waves incident on the hologram plane are numerically propagated. We verified this accelerated computational method theoretically and experimentally, and demonstrated optical reconstruction of a deep 3D image in which the effects of occlusions, transmission, refraction, and reflection were faithfully reproduced.