To generate ideal digital holograms, a computer-generated hologram (CGH) has been regarded as a solution. However, it has an unavoidable problem in that the computational burden for generating CGH is very large. Recently, many studies have been conducted to investigate different solutions in order to reduce the computational complexity of CGH by using particular methods such as look-up tables (LUTs) and parallel processing. Each method has a positive effectiveness about reducing computational time for generating CGH. However, it appears to be difficult to apply both methods simultaneously because of heavy memory consumption of the LUT technique. Therefore, we proposed a one-eighth LUT method where the memory usage of the LUT is reduced, making it possible to simultaneously apply both of the fast computing methods for the computation of CGH. With the one-eighth LUT method, only one-eighth of the zone plates were stored in the LUT. All of the zone plates were accessed by indexing method. Through this method, we significantly reduced memory usage of LUT. Also, we confirmed the feasibility of reducing the computational time of the CGH by using general-purpose graphic processing units while reducing the memory usage.