In order to analyze and process the random error of the fiber optic gyroscope (FOG) and improve its use precision, an error modeling method that combined empirical mode decomposition (EMD) and time series model was proposed. On the basis of the intrinsic mode functions (Imf) which was obtained by empirical mode decomposition, auto-regressive and moving average model (ARMA) modeling is performed hierarchically for each Imf. Then, Kalman filtering is performed layer by layer on the basis of the model to remove the random drift signals from the real angular velocity information. At the end of the algorithm, the signal which had been filtered need to be reorganized, and through the above steps, the conception of analyzing and modeling in connection with the random error of FOG from full frequency’s point of view was realized. Compared with other modeling methods, this method has a higher degree of simulation matching to the original data, at the same time, the experimental results have further shown that this method can effectively remove the signal of random drift from the fiber optic gyroscope’s output signal and improve its use precision significantly.