Large megawatts offshore wind turbine (OWT) with low natural frequency and low damping is subjected to significant vibration from wind and wave actions in its service environment. The one-dimensional prestressed tuned mass damper (PSTMD) is further extended to a 3D-PSTMD for the control of vibrations of the OWT in this paper. A multiple DOFs coupled system of turbine, blades, tower, and foundation under aerodynamic and hydrodynamic forces is considered in this study of vibration mitigation at fore-aft and side-side directions. The dynamic model is derived with the Lagrangian equation, and the superiorities of the PSTMD are proved from the perspective of theoretical analysis. Aerodynamic and hydrodynamic loads are generated with the blade element momentum (BEM) theory and Morrison equation, and the dynamic responses of different systems are computed by using the Wilson-θ method. The analysis results indicate that a damping coefficient of the 3D-PSTMD corresponding to the first vibration mode can be tuned to take up values larger than that in traditional three-dimensional pendulum (TMD) (3D-PTMD). The bidirectional vibration suppression competences of the 3D-PSTMD in the dynamic responses when under aerodynamic and hydrodynamic loads are better than those of the traditional 3D-PTMD.