As white noise, random drift is a key essential affecting the precision of laser gyro. Digital filtering can reduce the effect of the random drift. Some familiar digital filtering methods are studied in the article, i.e. the AR (2) model, Kalman filtering, wavelet analysis and wavelet packet analysis. The effects of different filtering methods are analyzed and compared with both power spectrum and Allan variance. Experiments indicate that Kalman filtering can achieve best performance as to filtering the random drift of ring laser gyro, and high frequency noise can be filtered to some extent by using wavelet analysis and wavelet packet analysis. These results are useful to the applications of laser gyro.