We propose a new look- up table algorithm, named trigonometric look- up tables (T- LUT) method to increase the speed of coherent ray trace (CRT）algorithm in generating holograms. The proposed algorithm is based on the original ray tracing method. By using a series of mathematical approximation changes and identical transformations, we generate a pure phase look- up table. This look- up table has three- dimensional features, fast generating speed, high precision, less memory capacity and so on. The new method overcomes CRT′ s shortcomings in computing the phase repeatedly. We implement T- LUT on graphics processing unit (GPU) using parallel computing by compute unified device architecture (CUDA), and optimize it three times. After algorithm optimizing, a series of experiments are carried out to verify the results by using a single GPU card. Our results indicate that the T- LUT algorithm can effectively shorten the computing time without sacrificing the quality of hologram reconstruction. Due to the different quantities of spatial samples, the speed has increased 30 to nearly a thousand times compared with original ray tracing algorithm implemented on GPU.