This study presents a novel adaptive control scheme for variable-speed wind turbine (VSWT) driven permanent magnet synchronous generator (PMSG) to ensure its operation under different operating conditions. The adaptive control scheme is based on the affine projection algorithm (APA) which provides a faster convergence and less computational complexity than the least-mean-square algorithm. The proposed adaptive controller is used to control both the generator-side converter and the grid-side inverter without giving additional tuning efforts. Each vector control scheme for the converter/inverter has four APA-based adaptive proportional-integral (PI) controllers. Detailed modelling and the control strategies of the system under study are demonstrated. Real wind speed data extracted from Hokkaido island, Japan is used in this study. The dynamic characteristics of a grid-connected VSWT-PMSG are investigated in details to ensure the proposed controller operation under different operating conditions. The effectiveness of the proposed adaptive controller is compared with that obtained using optimised PI controllers by Taguchi method. The validity of the adaptive vector control scheme is verified by the simulation results which are performed using PSCAD/EMTDC environment.