The maximize energy captured from the wind of a grid-connected variable speed Wind Energy Conversion System (WECS) based on a Permanent Magnet Synchronous Generator (PMSG) is investigated in this paper. An adaptive back-stepping control scheme is applied to achieve maximum power point tracking in the coefficient of maximum power. The features of the proposed control scheme are that it deals with the random nature of wind speed, the uncertainties and external perturbations the acting on WECS effectively, where the bounds of the perturbations are not known in advance. At the same time, a proof of the convergence of the closed-loop system under the proposed controller is derived using the Lyapunov stability theory. Finally, simulations are conducted to illustrate the effectiveness of the proposed approach. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.