To address the threat of harmful vibrations of semisubmersible floating offshore wind turbine （FOWT） in complex deepsea environments to the safety and durability， a design of distributed tuned mass dampers （TMDs） is proposed to control the plat? form pitch motion under the randomly combined wind and wave excitations， in combination with the geometric structure of the 5MW prototype of NREL in the United States. The distributed TMDs are installed inside the platform to form an equilateral trian? gle arrangement. To better describe the performance of the distributed TMDs on the semisubmersible FOWT， a 9-degree-of-free? dom multi-body dynamics model is proposed and established for the coupled semisubmersible FOWT-TMDs system based on La? grange's equation and the modal superposition method. Based on the H∞ algorithm， whose optimization objective is the peak value of the frequency response function of platform pitch motion， the parameters of the distributed TMDs are optimally designed， where the coupling relationship between multiple TMDs is considered. The numerical simulation of the coupled FOWT-TMDs system under the combined wind and wave excitations is carried out to analyze the performance of the distributed TMDs on the platform pitch response of the wind turbine. The results show that the distributed TMDs with optimal design has good damping performance on the platform pitch motion of the semisubmersible FOWT. Under random wind and wave loads in three different working condi? tions， the peak and standard deviation vibration reduction rates of the power spectral density curve near the natural frequency of platform pitch can reach more than 39% and 52%， respectively. The research method and results can provide reference for dynam? ic analysis and vibration control design of large semisubmersible FOWT.