The design principle and realization of a real FFT algorithm were proposed. In the proposed algorithm, real FFT computation of 2N points were transformed to complex FFT computation of N points according to the symmetry of input serial at first. Then after properly processing the N complex outputs of FFT, the 2N FFT complex outputs of original real inputs were gotten. The proposed algorithm can almost half reduce the operation time of FFT and resolve the conflict between the request of real-time operation in digital signal processing system and the lots of accounting in FFT. The software design of real FFT based on TMS320VC5402 DSP was given. The code length and operation time of the real FFT with 16, 32, 64, 128, 256, 512,1024 points were compared with that of complex FFT. The experiment results proved the correctness of the method.