Cable-driven parallel robots (CDPRs) possess a lot of advantages over conventional parallel manipulators and link-based robot manipulators in terms of acceleration due to their low inertia. This paper deals with under-constrained CDPRs, which manipulate the end-effector to carrying the payload by using a number of cables less than six, often used preferably owing to their simple structures. Since a smaller number of cables than six are used, the end-effector of CDPR has uncontrollable degrees of freedom and that causes swaying motion and oscillations. In this paper, a scheme to curb on the unwanted oscillation of the end-effector of the CDPR with three cables is proposed based on multimode input shaping. The precise dynamic model of the under-constrained CDPR is obtained to find natural frequencies, which depends on the position of the end-effector. The advantage of the proposed method is that it is practicable to generate the trajectories for vibration suppression based on multi-mode input-shaping scheme in spite of the complexity in the dynamics and the difficulty in computing the natural frequencies of the CDPR, which are required in any input-shaping scheme. To prove the effectiveness of the proposed method, computer simulations and experiments were carried out by using 3-D motion for CDPR with three cables.