This paper describes the design of a self-scheduled current controller for doubly-fed induction generators in wind energy conversion systems (WECS). The design is based on viewing the mechanical angular speed as an uncertain yet online measurable parameter and on subsuming the problem into the framework of linear parameter-varying (LPV) controller synthesis. An LPV controller is then synthesized to guarantee a bound on the worst-case energy gain for all admissible trajectories of rotor speed in the operating range. Furthermore, this study investigates the robust performance of the LPV controller with respect to other bounded machine parameter variations and the impact of the stator voltage dips on the robustness of the control system. Two closed loop simulation models, one with a conventional control scheme and the other with an LPV control scheme, are developed for the control of the electrical torque and the power factor on the rotor side in order to compare the performance of the control systems. Some simulation results are given to demonstrate the performance and robustness of the control algorithm.