Abstract: In allusion that classical Allan variance cannot highlight the nonstationary of stochastic errors of Fiber Optical Gyroscope (FOG), and Dynamic Allan Variance (DAVAR) can, but there was no theory which proved the validity and the effectiveness of DAVAR systematically. The DAVAR, a measure of the time -varying stability of FOG was presented and discussed. First, the classical Allan variance and DAVAR were mathematically defined, and then their behaviors were extensively tested on simulated and experimental FOG output signal. What' s more, FOG stochastic errors changes were quantitatively described by a two-dimensional method. Results prove the validity and effectiveness of the proposed new tool using for analyzing the stochastic errors of FOG. DAVAR analysis method not only can determine the coefficients of FOG stochastic error, but also can describe their non -stationary. DAVAR is a more comprehensive, more effective and more useful tool for judging FOG performance.