Abstract: Random drift is one of the main errors in fiber optical gyroscope (FOG). Modeling and revising random drift is an efficient method to improve system accuracy in filtering. Based on Allan variance, the differential equation model(DEM) of random drift is required to solve the shortages of traditional models which are time-consuming and over sensitive. In this paper, the power spectrum density (PSD) function was exploited to figure out the stochastic differential equation (SDE) of every noise. By using Allan variance to calculate the parameter of every noise and substituting the parameter in SDE which was driven by white noise, the random drift model was established. Experiment result illustrates that, the fitting error of random drift is no more than 8.6%，far lower than the traditional one of 58.3％. It is an effective method to build error model of random drift for FOG.