A vibration suppression control method for a ball screw driven flexible link is studied aiming at the phenomenon of residual elastic vibration in the stages of acceleration，decelerating and stopping under a flexible link load. The frequency excitation method and the least squares method are used to identify the natural resonant frequency of the flexible link acceleration and the dynamic model parameters of the ball screw driven flexible link system of the motor∶rmoment of inertia and friction coefficient. On this basis，the input shaping method is used to plan the acceleration signal，and the amplitude of the signal is reduced in the natural resonance frequency region of the flexible link in the planned acceleration signal to avoid exciting the natural resonance. The acceleration signal of the link is estimated according to the dynamic model of the flexible link，and the flexible link vibration suppression controller to export the resonance torque compensation signal is designed by using the generalized minimum variance control method to suppress the vibration caused by bending deformation of the connecting rod in running process. Finally，the experiment is carried out on a built experimental platform of ball screw slider driven flexible link. The experimental results show the effectiveness ofthe research method.