Abstract: Random drift is a main error of fiber optic gyro (FOG), it is a efficient method to reduce the random drift and improve the accuracy by modeling and compensation from the output of FOG. The static output of FOG is a random project, the steability and randomicity are analysised, the trend and periodicity is suited and compensated. The random drift of FOG is modeled by time series analytical method, the type and ladder are identificied by the autocorrelation function. The coefficient of the model is estimated by the least square, the FOG random drift model is AR(2). The raw data is compensated with the model, and the validity of the model is tested .It is shown that the result is greatly improved, and the random drift is efficiently reduced, the accuracy of the FOG is greatly improved. The model also is as the state of Kalman filter in the inertial navigation system.