A novel kind of adaptive second order sliding mode control algorithm, based on super-twisting control law (STW), is proposed and applied to a floating wind turbine (FWT). This new algorithm, for which the controller gains are dynamically adjusted with respect to the uncertainties and perturbations, has a very reduced number of tuning parameters versus previous adaptive versions of STW, and low-requirement computational requirement. This new controller is particularly well-adapted to the FWT control problems because the achievement of an accurate modeling of such system is a hard task; furthermore, it strongly reduces the tuning effort with respect to previous adaptive versions of STW. The proposed algorithm is implemented on a FAST nonlinear FWT model in the SIMULINK environment, and the performances are compared with the standard gain scheduling PI (GSPI) control and the original adaptive STW. The results show high performances of the proposed controller for rotor speed regulation and reduction of platform pitch motion.