The FPGA realization of a floating-point FFT processor is proposed to get over the poor precision of the fixed-point FFT processor.The definition of the floating-point format,the selection of arithmetic and the key techniques of the FPGA realization are discussed. Such a processor has been put into service and has stable performance. Its operating frequency is 80MHz and it can finish 1024 point FFT/IFFT in 64μs with an error less than -80dB.