The influence of Kerr effect to close-loop digital resonator fiber optic gyroscope based on square-wave frequency modulation was analyzed in theory.The results show that the Kerr-effect-induced bias relates to the light intensity difference between two inverse lightwaves,and the amplitudes of square-wave frequency modulation of these inverse lightwaves also affect it.Through proper adjustment to frequency modulation amplitude,the Kerr-effect-induced bias can be effectively reduced.This method for Kerr-effect-induced bias reduction utilizing the characteristic of square-wave frequency modulation,need without any additional optical devices,has low intensity modulation frequency requirement.And it is a effective method for Kerr-effect-induced bias reduction in close-loop digital R-FOG.