Based on the mechanism of Kerr effect in Brillouin Fiber-optic Ring Resonator(BFRR), the resonant cavity characteristic is researched theoretically when considering the Kerr effect, in order to get the possibility of occurrence of first-order Stokes light optical bistability. Experiments show that the optical bistability in 30 meters short cavity happens while input light intensity is about 440 μW, and the bistability is related with coupling coefficient and the insertion loss of the cavity coupler. Secondly, the Kerr effect in BFRR of Brillouin Fiber-optic Gyroscope (BFOG) is analyzed, focusing on the influence of resonant deviation on gyroscope nonlinear output and dynamic working range. Furthermore, the double-loop BFOG program is proposed, which provides a potential solution of Kerr effect error in Brillouin fiber-optic gyroscope.