Allan variance method is an effective tool for the analysis of the fiber optic gyro (FOG) static noise, but it only applies to stationary signals and can′t reflect the dynamic characteristics of FOG. In order to comprehensively study on FOG random error, dynamic Allan variance (DAVAR) is used to analyse the high precision FOG. The mathematical foundations of the DAVAR are presented and discussed, and the measured data under vibration and variable temperature conditions are obtained respectively, and the noise of which is calculated through DAVAR, its effectiveness is shown by performing extensive numerical analyses on simulated and experimental data. Experimental results show that the DAVAR analysis method can not only determine the proportion of the various noise factors, but also identify and refine the FOG noise in mutation environment, and the Allan variances are visually reflected in a 3D graph. The results prove the validity and the effectiveness of the proposed new tool.