The passive tunned mass dampers (TMDs) can effectively mitigate vibrations of offshore wind turbines (OWTs). However, most of the aforementioned literatures only focus on the vibration reduction effect of a TMD without considering vibration mechanism of the OWT with and without the TMD, which is affected by the frequency characteristics of wind-wave loadings, especially the low frequency characteristics of wind loads. Moreover, the baseline control of OWTs including the pitch control and the generator torque control can affect the dynamical responses of the OWT and thus the vibration reduction performance of a TMD. In this paper, an optimal dual TMD is placed at the nacelle for mitigating the vibration of the OWT. The influence of the TMD on dynamical responses of the OWT is fully investigated under the baseline control and the various wind-wave loadings. The research shows that the TMD has an excellent vibration reduction effect when the OWT is parked (at high wind velocities). When the OWT is parked and the wind velocity at the hub is at 25 m/s, the vibration reduction performance of the TMD is the best, and the maximum values of the tower top displacement and acceleration, and the top and the bottom tower moments are reduced by 25.41%, 24.76%, 7.09% and 16.78%, respectively. Moreover, the optimal designs for the TMD are further conducted under the baseline control and the different wind-wave loadings. The research results show that the vibration reduction performance of the TMD is not significantly enhanced when the OWT can work normally, but it is enhanced when the OWT is parked. This work can provide technical support for optimal design of the TMD under the wind-wave environments.