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 MPC-LPV scheme is validated via simulation and it is compared with another MPC scheme based on linearized models of the system.