The non-linear motion characteristics of the large-scale floating wind turbine have been significantly enhanced. For this reason, the DTU 10 MW wind turbine was used as the research object, and the NAUTILUS semi-submersible platform floating wind turbine model was established, and the tuned mass damper（TMD） was installed in the nacelle Optimize TMD parameters through multi-island genetic algorithm, study the motion response characteristics of floating wind turbines without TMD control, TMD control（unoptimized） and optimized TMD control, and based on chaos theory, adopt phase space reconstruction and maximum Lyapunov exponent method from qualitative and quantitative analysis of the nonlinear characteristics of floating wind turbine motion response. The results show that under TMD control and optimized TMD control, the forward to after displacement response of the floating wind turbine tower top is significantly reduced, but the side to side displacement response is relatively small; the peak forward to after acceleration response of the tower is significantly reduced in the range of 30 m～90 m. The peak value of side to side acceleration response decreases in the range of 10 m～30 m. Compared with the non-TMD control, under the optimized TMD control, the chaotic characteristics of the floating wind turbine’s motion response are weakened, and the maximum Lyapunov exponents are all reduced, indicating that the optimized TMD can reduce the nonlinear characteristics of its motion response.