The paper deals with the control of variable-speed wind energy conversion systems (WECS) in the context of linear parameter varying (LPV) systems, a recent formulation of the classic gain scheduling technique. The LPV approach is specially useful in variable-speed WECS control, which is characterized by nonlinear dynamic behavior and opposite objectives. In particular, the following objectives are considered: conversion efficiency maximization, safe operation, resonant modes damping, and robust stability. The proposed LPV controller is compared with a fixed controller that also takes into account the nonlinear behavior of the wind turbine.