FFT (fast Fourier transform) plays a very important role in many fields, such as digital signal processing, digital image processing and so on. However, in application, FFT becomes a factor of affecting the processing efficiency, especially in remote sensing, which large amounts of data need to be processed with FFT. So shortening the FFT computation time is particularly important. GPU (Graphics Processing Unit) has been used in many common areas and its acceleration effect is very obvious compared with CPU (Central Processing Unit) platform. In this paper, we present a new parallel method to execute FFT on GPU. Based on GPU storage system and hardware processing pipeline, we improve the way of data storage. We divided the data into parts reasonably according the size of data to make full use of the characteristics of the GPU. We propose the memory optimized method based on share memory and texture memory to reduce the number of global memory access to achieve better efficiency. The results show that the GPU-based memory optimized FFT implementation not only can increase over 100% than FFTW library in CPU platform, but also can improve over 30% than CUFFT library in GPU platform.