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The floating platform motion of an offshore wind turbine system can exacerbate output power fluctuations and increase fatigue loads. This paper proposes a new scheme based on a fast second-order sliding mode (SOSM) control and an adaptive super-twisting extended state observer to suppress the platform motion and power fluctuation. Firstly, an affine nonlinear model of the floating wind turbine pitch system is constructed. Then, a fast SOSM pitch control law is adopted to adjust the blade pitch angle, and a new adaptive super-twisting extended state observer is constructed to achieve total disturbance observation. Finally, simulations are conducted under two cases of wind and wave conditions based on FAST (fatigue, aerodynamics, structures, and turbulence) and MATLAB/Simulink. Compared with the traditional proportional integral (PI) control scheme and standard super-twisting control scheme, the platform roll under the proposed scheme is reduced by 13% and 4%, and pitch is reduced by 16% and 3% in Case 1. Correspondingly, the roll is reduced by 9% and 15%, and pitch is reduced by 7% and 1% in Case 2. For the tower top pitch and yaw moment, load reductions of 7% and 3% or more are achievable compared with those under the PI control scheme. It is indicated that the proposed scheme is more effective in suppressing floating platform motion, stabilizing output power of the wind turbine system, and reducing tower loads.