The classical dynamic Allan variance(DAVAR) can describe the non-stationary of random error of fiber optical gyroscope(FOG) effectively. However, the method has defects such as poor confidence on the estimation of long-term τ-values due to the reduced amount of data captured by the fixed length windows. Besides, the method is difficult to make a satisfactory tradeoff between dynamic tracking capabilities and variance reduction. An improved DAVAR algorithm based on kurtosis and data extension was proposed to solve the problems. Firstly, the kurtosis of data inside the windows was introduced as characterization of signal′s instantaneous non-stationary, and the window length function which was utilized to truncate the signal was built by taken kurtosis as variables, the function can make window length change with the non-stationary of the signal automatically. Secondly, the random error of FOG was truncated with the function. Then the data in the windows were extended by the total variance method to improve the confidence. At last the Allan variance of extended data was computed and arranged by three-dimensional. The measured data of FOG start-up signal was analyzed with the proposed algorithm and DAVAR. The results show that the proposed algorithm is an effective way to characterize non-stationary of FOG and can also obtain a lower estimation error at long-term τ-values.