Increasing numbers of FOWTs (floating offshore wind turbines) are planned in the coming years due to their high potential in massive generation of clean energy from ocean-wind. In the present study, a numerical prediction tool has been developed for the fully coupled dynamic analysis of an FOWT system in time domain including aero-loading, blade-rotor dynamics and control, mooring dynamics, and platform motions so that the influence of rotor-control dynamics on the hull-mooring performance and vice versa can be assessed. Hywind spar design with 5MW turbine is selected as an example, and two different environmental conditions, maximum operational and survival conditions, are applied for this study. The maximum operational condition means the maximum environmental condition that wind turbine can work normally, and the survival condition represents the extreme situation without any blade-turbine operation. Through this study, it is seen that the design environments for different structural components of FOWT can be different. The developed technology and numerical tool are readily applicable to the design of any future FOWTs in any combinations of irregular waves, dynamic winds, and steady currents.