The random drift is one of the most significant factors that can affect the navigation precision of fiber of gyroscope (FOG). At first, it can be found that its time-relativity was weak based on the auto-related-function analysis of FOG's output series. Then the parameters of linear AR-model and nonlinear AR-model were worked out by the function of Yule-Walker and LMS. At last, the models and their most suitable orders were chosen by both the filtered effect and applicable test. The results indicate that both AR(1)-model and NAR(1)-model are suitable for the FOG's random drift modeling and real-time filtering, and can improve the zero bias's stability obviously.