The tremendous wind-wave excitations bring about structural vibrations, which would have adverse influences on the power generation efficiency of the spar floating offshore wind turbine (FOWT). Therefore, two tuned mass dampers (TMDs) are installed in the platform and nacelle of the spar FOWT to control the vibration responses of the structure. The aero-hydro-servo-structure-TMDs coupling kinetics model of 16-degree-of-freedom (DOF) is firstly established for the spar FOWT. The correctness of the coupled model is then verified through comparing with OC3 project of FAST developed by the National Renewable Energy Laboratory (NREL). Subsequently, the TMDs stiffness and damping coefficients are optimized in constraints of the TMDs mass and stroke. Furthermore, the vibration reduction effects of TMDs are studied in the free decay state and wind-wave load cases, respectively. The simulation results demonstrate that the platform TMD can effectively reduce the platform pitch (PFPI) movement and low frequency vibration of the tower top fore-aft (TTFA) deflection, while the nacelle TMD is effective for the high frequency vibration of the TTFA deflection. Thus, the TMDs can control the structural vibration responses of spar FOWTs. (C) 2020 Elsevier Ltd. All rights reserved.