Based on the nonlinear coupled mode theory, by using the reversely recursive RungeKutta method, the influence of introducing the Lorentzian function perturbation to the magnetooptic coupling coefficient on the linear transmission spectrum and the bistable characteristics of magnetooptic fiber Bragg gratings is investigated numerically. The results of the study show that introducing the Lorentzian perturbation to the magnetooptic coupling coefficient can open up a narrow transmission window in the linear transmission spectrum stopband. The perturbation widths and the perturbation center positions can affect the position, the width, and the peak amplitude of the transmission window. The bistable characteristics can show significant differences when the perturbation widths and the perturbation center positions change. The bistable characteristics can be further optimized by choosing perturbation parameters reasonably.