The non-linear behaviour of wind turbines demands control strategies that guarantee the robustness of the closed-loop system. Linear parameter-varying (LPV) controllers adapt their dynamics to the system operating points, and the robustness of the closed loop is guaranteed in the controller design process. An LPV collective pitch controller has been developed within this work to regulate the generator speed in the above rated power production control zone. The performance of this LPV controller has been compared with two baseline control strategies previously designed, on the basis of classical gain scheduling methods and linear time-invariant robust H∞ controllers. The synthesis of the LPV controller is based on the solution of a linear matrix inequalities system, proposed in a mixed-sensitivity control scenario where not only weight functions are used but also an LPV model of the wind turbine is necessary. As a contribution, the LPV model used is derived from a family of linear models extracted from the linearization process of the wind turbine non-linear model. The offshore wind turbine of 5 MW defined in the Upwind European project is the used reference non-linear model, and it has been modelled using the GH Bladed 4.0 software package. The designed LPV controller has been validated in GH Bladed, and an exhaustive analysis has been carried out to calculate fatigue load reductions on wind turbine components, as well as to analyse the load mitigation in some extreme cases. Copyright © 2014 John Wiley & Sons, Ltd.