Remotely operated vehicle (ROV) system is significantly affected by the excitations coming from the top -end vessel motion and the environmental hydrodynamic forces. Especially, during initial deployment and final recovery stages, the relative motion between suspending ROV and moving top -end vessel gets more complicated and even larger. This may cause a body collision, and consequently the cable tension can also be severely changed by larger ROV motion. Sometimes, cable slack may occur, which seriously affects structural safety. To study the dynamic responses of ROV system induced by vessel heave during initial deployment and final recovery processes, the FEM numerical simulations, combining with the hydrodynamic model are conducted. Then the ROV displacement and cable tension time histories are presented. The influences of vessel motion amplitude and frequency, along with initial condition, on the dynamic responses of ROV system are also discussed. Moreover, to explore the dynamic behaviors of the ROV system further, we discuss the physical mechanisms driving response amplification through theoretical models. The governing equation of ROV system dynamics with a vertical moving boundary is established, and a dimensionless control parameter called amplitude -frequency factor, which characterizes the dynamic excitation effect of vessel heave, is proposed. Then, in order to study the influences of nonlinear hydrodynamic damping effect on ROV response, an empirical formula for hydrodynamic damping ratio is proposed based on ROV displacement time histories. Finally, under consideration of the nonlinear damping effect, the unstable regions of vessel motion amplitude and frequency at different initial conditions are obtained. The results show that the vessel heave may induce a parametric excitation response to the ROV system. Particularly, parametric resonance is most pronounced, when the vessel motion frequency is close to twice the natural frequency of the ROV system. While, under the nonlinear damping effect generated by hydrodynamic force, the parametric resonance occurs when the amplitude -frequency factor reaches its threshold. The unstable regions under hydrodynamic damping are smaller compared with that without damping. Furthermore, as the initial angular displacement of ROV increases, the unstable region becomes smaller further, or, in other words, the parametric conditions of vessel heave for ROV response amplification become more demanding.