This paper addresses the control of a variable-speed variable-pitch wind turbine in the whole wind speed range. To this end, a linear parameter varying anti-windup (AW) controller is proposed as part of a control structure focused on improving the transition between low- and high-wind speed operations. The control structure is similar to classical PI controls used in commercial wind turbines. However, a more advanced gain-scheduled controller and AW compensation are proposed. As a consequence, the new control scheme is capable of improving the behavior of the wind turbine in the transition zone and provides better stability margins. The proposed control was evaluated in a 5-MW wind turbine benchmark and compared with a classical control scheme. To this end, very demanding and realistic testing scenarios were built using the FAST aeroelastic wind turbine simulator as well as standardized wind speed profiles.