Compared with spar-buoy and tension-leg platform floating offshore wind turbines (FOWTs), the flexibilities in operating water depth promote generalized applications of semi-submersible FOWT. In this study, a passive structural control strategy of a tuned mass damper (TMD) design method for a semi-submersible FOWT was implemented to mitigate FOWT responses under combined winds and waves. A reduced coupled model of a semi-submersible FOWT with TMDs mounted in the nacelle and platform was established based on D'Alembert's principle. Sequentially, the parameters of the reduced coupled model were estimated using the Leven-Marquardt (LM) algorithm, and the simulation accuracy was validated by comparison with the related fully coupled model in OpenFAST. To minimize the standard deviation of tower-top displacement, the design of the TMD was optimized by genetic algorithm (GA) based on the reduced coupled model, and three different TMD configurations were proposed. Furthermore, the effectiveness of the optimized TMDs was evaluated based on a fully coupled model in OpenFAST under typical sea states. The optimized nacelle and platform TMDs could effectively suppress the tower fundamental and platform pitch frequencies, respectively. Moreover, improved mitigation effects were observed using the optimized multiple TMDs, which comprise local dampers installed in the nacelle and platform.