There are considerable literatures on the Bit Error Rate(BER)evaluation of DifferentialDetection of Gaussian Minimum Shift Keying(DDGMSK)system using Decision Feedback(DF),butmost of them give the performance based on the Monte Carlo Error Counting(MCEC)technique.Fromthe probability distribution of the phase angle between two vectors perturbed by Gaussian noises,theformulae of BER are derived for the performance analysis of DDGMSK system with DF in this letter.Considering the m-bit dock-tailed sequence,the new formulae of Gaussian Minimum Shift Keying(GMSK)modulated phase and the Time-Varying Signal to Noise Ratio(TVSNR)of the demodulatedsignal are presented,and it is proved that the relationship between the TVSNR of the demodulatedsignal and the size of eye opening is not inevitable.Simulation results show that the theoretical in-vestigation gives analogous results with the MCEC technique.The formulae presented are useful for theperformance analysis of systems using GMSK as modulating and demodulating method,for instance,the analysis of synchronous performance of frequency-hopping communication system. There are considerable literatures on the Bit Error Rate (BER) evaluation of DifferentialDetection of Gaussian Minimum Shift Keying (DDGMSK) system using Decision Feedback (DF), but most of them give the performance based on the Monte Carlo Error Counting (MCEC) technique. Flash probability distribution of the phase angle between two vectors perturbed by Gaussian noises, theformulae of BER are derived for the performance analysis of DDGMSK system with DF in this letter. C onidering the m-bit dock-tailed sequence, the new formulae of Gaussian Minimum Shift Keying (GMSK) modulated phase and the Time-Varying Signal to Noise Ratio (TVSNR) of the demodulated signals are presented, and it is proved that the relationship between the TVSNR of the demodulated signals and the size of eye opening is not inevitable. Simulation results show that the theoretical in-vestigation gives analogous results with the MCEC technique. formulae are useful for the performance analysis of systems using GMSK as modulating and demodulating method, for instance, the analysis of synchronous performance of frequency-hopping communication system.