This paper deals with the elasto-dynamic model-based control of Cable-Driven Parallel Robots (CDPRs), which manifests in the coupling of a PID feedback controller with a model-based feed-forward control scheme. The feed-forward controller is derived from an inverse elasto-dynamic model of CDPR, which compensates the end-effector dynamics and specifically its vibrations due to cable elasticity. The integration of cable tension calculation into this control strategy guarantees positive cable tensions along the trajectory. Simulations and experimentations while using a suspended and non-redundant CDPR show that tracking errors and vibrations can be reduced by the proposed strategy compared to conventional rigid-body model-based control.