The parameters design and vibration control of the system of Spar-floating offshore wind turbine (S-FOWT) coupled tuned mass damper-inerter (TMDI) under the joint wind-wave loads are studied in this paper. Firstly, the theoretical model of 15-DOF Spar-FOWT with high fidelity is established based on multi-body dynamics modeling method and compared with FAST from both cases of damped free vibration and forced vibration. Furthermore, the damping efficiency of the FOWT-TMDI system under wind and wave loads is analyzed. In order to obtain the global optimal system parameters, the surrogate model method is used to optimize the time-varying and fully-coupled system. An example analysis shows that the model of 15-DOF Spar-FOWT has high fidelity which accurately secures the global dynamical characteristics of the wind turbine system; meanwhile, the TMDI optimized by the proposed method has the expected control effect and the desired objective of "reduction in mass and stroke" is achieved. Compared with TMD, in addition, the TMDI has anticipative efficiency of the vibration reduction while reducing 75% of the mass and reducing about 80% of the damper stroke.