Kerr effect is one of the key factors limiting the performance of the resonator fiber optic gyroscope (RFOG). Based on the Kerr effect and Sagnac effect, we establish a theoretical model of gyroscope Kerr effect bias error of RFOG, and analyze the influence of difference of coupling ratio of the output couplers in clockwise and counter-clockwise beam paths in fiber resonator and the difference of lengths of two resonant cavity arms on the performance of the gyroscope. In addition, we also present a scheme to suppress the Kerr effect bias error by coupling light intensity control and structure design of the RFOG. After 4 runs of individual experiments, it is shown that the proposed scheme can effectively suppress the Kerr effect. The gyroscope bias is reduced from 0.150 (°)/s to 0.017 (°)/s, and the bias stability is increased from 1300 (°)/h to 140 (°)/h. The gyroscope performance can be improved by nearly one order of magnitude.