In view of the hemispherical resonator gyro(HRG) random error which affects measurement accuracy of inertial measurement unit, An improved processing method based on autoregressive and moving average (ARMA) model and adaptive Kalman filter(AKF) is proposed in this paper. First of all, the autocorrelation and partial correlation of the pretreated data is analyzed to determine the applicable model of the random error. Then the BIC rule is used to estimate the order of ARMA model, the model parameter is acquired through long autoregressive model residual error calculating method, the weighted adaptive factor is introduced to adjust online step prediction matrix and measure matrix which is used to improve filter equation. Finally, the five main error coefficients are compared. The result shows that the modified algorithm can effectively restrain the random error, which provides a new way for HRG random error modeling compensation.