The static time drift of MEMS accelerometer was studied through theory and experiments,and a BM wavelet packets general regression neural network(GRNN) was developed to compensate the drift. The first,the error of the drift was removed by the wavelet packet based on the Birgé Massert improved function,the second, the zero drift model of the MEMS accelerometer was established based on GRNN,which has a good approximation capability,fast learning speed and excellent network stability. The computer results show that this model can compensate the zero drift effectively.Comparing with the original data, compensation with least square fitting and compensation only by GRNN, the mean values of zero drift is reduces by 97.4%, 67.8%, 67.8% respectively;the variance reduces by 87.4%, 87.5%, 90.9%, respectively.The delay time of the model is 10-5s.The results illustrate the feasibility and validity of the Birgé Massert Wavelet Packers General Regression Neural Network model.