Abstract: The compensating method for micro-electro-mechanical systems(MEMS) gyroscopic random drift error is discussed from the point of view on practical applications.Based on the principle of the time-sequence analysis from the random series,the original measurement from the MEMS gyroscope is pretreated by an real time average estimation algorithm to get random drift signals.The residual signal is modeled by an AR model and is filtered by Kalman filtering.The compensating results for the practical testing data of an MEMS gyroscope show that the drift error can be effectively reduced by using the filtering method presented,and the measurement accuracy in practice can be further improved.