This study presents a successful application of a model predictive control (MPC) design approach based on linear parameter-varying (LPV) models subject to input/output constraints to control a utility-scale wind turbine. The control objectives are to allow the wind turbine to extract from the wind the rated power taking into account the wind speed variation, to reduce mechanical loads and power fluctuations and to guarantee the stability of the system for the whole range of operation. A modified min–max MPC-LPV scheme is proposed to compute online the optimal control input at each sampling instant by solving an optimisation problem subject to linear matrix inequality constraints. To reduce the conservatism of the original MPC scheme due to the overbounding associated with affine parameter-dependence, the full block S-procedure with a linear fractional transformation formulation is used. The performance and the efficiency of the proposed MPC-LPV algorithm is validated via simulation and compared with the original scheme and other conventional controllers.