In this paper, a new approach is proposed for the efficient generation of computer-generated holograms (CGHs) using the spatially redundant data on a 3D object and the novel look-up table (N-LUT) method. First, the pre-calculated N-point principle fringe patterns (PFPs) were calculated using the 1-point PFP of the N-LUT. Second, spatially redundant data on a 3D object were extracted and re-grouped into the N-point redundancy map using the run-length encoding (RLE) method. Then CGH patterns were generated using the spatial redundancy map and the N-LUT method. Finally, the generated hologram patterns were reconstructed. In this approach, the object points that were involved in the calculation of the CGH patterns were dramatically reduced, due to which the computational speed was increased. Some experiments with a test 3D object were carried out and the results were compared with those of conventional methods.