An acquisition method of GPS signals based on fast Fourier transform (FFT) is proposed. The method applies Winograd Fourier transform algorithm (WFTA), prime factor FFT algorithm (PFA) and Cooley-Tukey FFT algorithm to perform FFT on the GPS IF signal samples. According to the characteristics of those three algorithms, large number point FFT can be decomposed into small number point FFT. Therefore, the number of the samples in FFT computation is arbitrary. Compared with the subsample-based methods, such as zero padding, linear interpolation, sinc interpolation and averaging correlation method, the proposed method remains all the correlation information since it saves all the IF signal samples. At last, computer simulation is performed to validate this code acquisition method and test the performance.