This paper demonstrates the application of a low conservative model predictive control (MPC) scheme based on linear parameter-varying (LPV) models to control a utility scale wind turbine. The main objective of the controller is to allow the wind turbine to extract from the wind a prespecified desired amount of power according to the wind speed and to guarantee the stability of the closed-loop system during the whole range of operation. An LPV representation for a nonlinear model of a 225 KW wind turbine is developed using the Jacobian linearization based technique. A tight parameter set is considered to reduce the conservatism of the LPV model. Then a quasi min-max MPC-LPV algorithm is used to compute online the optimal control input at each sampling instant. The performance and the efficiency of the MPCLPV scheme is validated via simulation and it is compared with another MPC scheme based on linearized models of the system.