MEMS gyroscope is a new type of inertial device with small size, low cost, light weight, high reliability, but less precise and random error is relatively large. In this paper, from a practical engineering application point of view, first, the MEMS gyroscope random errors is real-time average filtered. Then, based on the basic principle of time series analysis of random sequence , the first-order AR model of MEMS gyroscope random errors is established. Finally, based on Markov characteristic of kalman filtering algorithm, each output of the MEMS gyroscope is multiple real-time filtered. Through the specific data processing, MEMS gyroscope random errors reduced to about two per cent of the original.