Abstract: A prime factor DFT Algorithm for 840 Complex data is presented in this paper. It transforms the operation of the 840points DPT to the operation of the prime factor 3,5,7,8 points DPT. It is pointed out that the Winograd small DFT algorithm can be cited directly for the Short N DFT calculation of the prime factor 3,7,8 without unscrambling. However the only need is reordering the results of the 5 points DPT according to the residue representation <3k>₅. The Flowchart and the BASIC Program list of the prime factor DPT algorithm for 840 complex data are given in this paper. At last, the performing of the program by using a 8-bits microcomputer is presented here, and several methods for increasing the calculating rate are then pointed out.