In order to comprehensively understand the characteristics of random drift of fiber optic gyro (FOG) varying with time, the characteristics of the random error terms of FOG utilizing the dynamic Allan variance (DAVAR) method are studied. The results show that, the DAVAR not only can accurately assess each error of FOG, but also can directly reflect the error stability of FOG. As the DAVAR needs to estimate the Allan variances at all time points, the computational time of the DAVAR grows very quickly with the increase of the analyzed time series. In order to solve the problem, a improved fast DAVAR algorithm based on the choice of relevant time t for the computation of the DAVAR is proposed. The results show that the improved fast DAVAR algorithm dramatically reduces the computational time without affecting operation results.