A pipelined FFT processor designed for fast and real-time requirements with FPGA is introduced. This FFT processor can be used to real-time frequency analysis and its working frequency can reach to 75 MHz. The leakage error is reduced through multiply the sampled signal by a weighting window. In order to improve FFT's working frequency and economize FPGA resources, an algorithm of 1024-point complex to compute 2048-point real data is adopted. In addition, an approximate algorithm to compute module value of complex number is introduced.