Fiber optic gyro (FOG) is an optical gyroscope which is based on the Sagnac effect and uses the optical fiber coil as light propagation channel. Gyro drift consists of two components: systemic drift and random drift. Systemic drift can be compensated by testing and calibrating. Random drift changes with time, so it becomes an important indicator to measure the precision of gyroscope, which has a great impact on the inertial navigation system. It can’t be compensated by the simple method. Random drift is a main error of fiber optic gyro (FOG). The static output of FOG is a random project and it has more random noise when as the inertial navigation sensor, which will affect the measurement accuracy. It is an efficient method to reduce the random drift and improve the accuracy by modeling and compensation from the output of FOG. According to the characteristic of fiber optic gyro, the random drift model is studied. Using the time series method, the constant component of the random noise original data is extracted. After stationarity and normality tests, a normal random process is acquired. Based on this, the model is established using the recursive least squares, and then the model is applied to the normal Kalman and adaptive Kalman, finally the data is process with the filter. After experimental verification, the noise variance was reduced after filtering, and the effect is obvious.