In this paper, adaptive high order sliding mode (HOSM) based control schemes are proposed for a floating offshore wind turbine (FOWT). These adaptive control methods are especially efficient for systems with uncertainties and external perturbations that is well adapted to wind turbines systems. The two HOSM based controllers are applied on FOWT, their main features being that they require a very reduced knowledge of the system (only the relative degree is supposed known) and a reduced tuning effort compared to standard controllers for FOWT as gain scheduled PI (GSPI) controller. Simulation results show high performances of the proposed controllers for rotor speed regulation and reduction of platform pitch motion.