This paper presents a model-based super-twisting controller for a 5 MW floating wind turbine mounted on a tensioned-leg platform. For the design of the super-twisting controller, a control-oriented model is selected in the literature and adapted to be written as a function affine in control. The proposed controller is designed for the regulation of the rotor speed at its rated value while reducing the platform pitch angle oscillations. The control law has been validated on a high accuracy simulation code OpenFAST with four different scenarios. The simulation results have shown that the super-twisting algorithm is able to regulate the rotor speed and to mitigate platform oscillations for different wind and wave conditions.