In order to solve the vibration problem of low-damping flexible mechanism in motion, a cascade vibration suppression trajectory planning method combining the advantages of optimal double S-shape trajectory and input shaping method is proposed. The advantage of this method is that it can effectively suppress the vibration in the period of uniform motion. The correctness of this method is proved by theoretical analysis and digital simulation. Finally, the application results of the proposed method in the FAST feed support system show that this method can effectively improve the motion accuracy of the parallel cable mechanism, especially the position tracking accuracy can be improved over 20% when the speed is constant.