Abstract: This paper presents a new prime factor algorithm of FFT in which data can be calculated in place or non in place and in the order with no input-output scrambling or in the order with scrambling. The algorithm presented is different in structure from the traditional prime factor algorithm and requires address translation of intermediate data module while each one dimensional small scale DFT of multidimensional DFT is calculated. Analysis and experiment on the computer show that, as compared to the traditional prime factor algorithm, scrambling operation is not necessary in the new algorithm, in which computation can be mode in place, in sequential order, with less storing units and improved computing speed.