Abstract: In order to study the control problem of chaotic motion of 7-degree-of-freedom spur bevel wheel transmission system, the centralized mass method is used to establish the dynamic model of the gear system, and the Runge-Kutta method is used to solve the law of the transition from periodic motion to chaotic motion in the parameter interval.According to the chaotic motion of a specific parameter region, the disturbance of the control parameters of the system is used as the output of the fuzzy neural network, and the Euclidean distance of the Poincaré section of the system is used as the input, and the fuzzy neural network controller is constructed.To solve the problems that particle swarm optimization（PSO） is prone to fall into local optimum and has poor convergence, an improved PSO algorithm is proposed based on the adaptive Lévy flight mechanism with dynamic center migration and self-adaptive parameters.This improved algorithm is used to optimize the parameters of a fuzzy neural network controller and achieve rapid convergence, thus avoiding the blindness of controller parameters.Numerical simulation shows that the control strategy stabilizes the phase trajectory to periodic motion, and the method provides a universal solution for the nonlinear vibration control of the bevel gear transmission system.