Flexible manipulators have been widely used in industrial production. However, due to the poor rigidity of the flexible manipulator, it is easy to generate vibration. It will reduce the working accuracy and service life of the flexible manipulator. It is necessary to suppress the vibration during the operation of the flexible manipulator. Based on the energy method and Hamilton principle, the partial differential equations of the flexible manipulator are established. Secondly, an improved radial basis function (RBF) neural network is combined with the fuzzy backstepping method to identify and suppress the random vibration during the operation of the flexible manipulator, and the Lyapunov function and control law are designed. Finally, Simulink was used to build a simulation platform, three different external disturbances were set up, and the effect of vibration suppression was observed through the change curves of the final velocity error and displacement error. Compared with RBF neural network boundary control method and RBF neural network inversion method, the simulation results show that the effect of RBF neural network fuzzy inversion method is better than the previous two control methods, the system convergence is faster, and the equilibrium position error is smaller.