The conventional computer-generated hologram reconstructing photorealistic three-dimensional (3D) images based on ray-wavefront conversion has the disadvantage of spatio-angular resolution trade-off. In this Letter, we propose for the first time, to the best of our knowledge, a computer-generated photorealistic hologram without spatio-angular resolution trade-off based on the additive compressive light field (CLF) approach. The original light field is compressed into multiple layer images through numerical optimization based on the additive light field principle. Then, by independently calculating the wave propagation from each layer image to the hologram plane and adding them together, a CLF hologram is generated. Since the CLF information is presented through a holographic method, the advantage of high resolution in CLF is preserved while the limitation of the number of physically stacked layers (such as liquid crystal displays) is removed, leading to higher quality, larger depth of field, and higher brightness compared with a conventional CLF display. The proposed method is verified with a photorealistic optical experiment.