The fiber optic gyro(FOG) strapdown inertial navigation system(SINS) is researched. Auto-regressive moving average(ARMA) model is built for modeling stochastic errors in FOG by using time series analysis method. The FOG stochastic model is realized in SINS self-alignment. Real-time filtering of FOG stochastic error is realized in the process of SINS gyrocompass self-alignment. The prototype test results show that the proposed method can effectively improve the accuracy of FOG SINS gyrocompass self-alignment.