For fiber optic gyroscope(FOG), the bias stability is an important index to measure its performance level , which directly affects the accuracy of FOG , and affects the initial alignment accuracy and navigation accuracy of FOG inertial navigation system. Therefore, the requirement of the high precision FOG on the bias stability is rising. Due to the conduction of power and the space electromagnetic radiation of circuit, there is unavoidable cross-coupling between the forward channel circuit, the backward channel circuit and the light source driving circuit in the FOG, and these cross-coupling have a certain extent influence on the performance of the FOG. As the cross-coupling coefficient changes in different environments, the FOG bias bring out drift. In this paper, the internal cross-coupling model of FOG is established. Aiming at the bias drift caused by cross-coupling, a suppression method was proposed, which eliminate the bias drift by periodically converting the polarity of Y-waveguide and the corresponding modulation and demodulation algorithm. A large number of tests were carried out at high temperature and low temperature. The experimental results show that the bias drift of FOG is reduced from 0.31°/h to 0.07°/h at different temperature points.