Abstract The Mixed Time and Frequency Decimation FFT Algorithm (MDFFT) proposed by K. Nakayama is simplified and deepened, then a new FFT algorithm based on tree-decomposition process is developed. The number of real multiplications of the newalgorithm is about (65/64)Nlog2N-3N-4 which is less than (3/2)Nlog2N-7N+10N1/2-4 of MDFFT.