FFT (Fast Fourier Transform) has been widely used in various fields such as image processing, voice processing, physics, astronomy, applied mathematics and so forth. Much research has been conducted due to the importance of the FFT and recently new FFT algorithms using a GPU (Graphics Processing Unit) have been developed for the purpose of much faster processing. In this paper, the new optimal FFT algorithm using the Pease FFT algorithm has been proposed reflecting the hardware configuration of a GPGPU (General Purpose computing of GPU). According to the experiments, the proposed algorithm outperformed by between 3% to 43% compared to the CUFFT algorithm.