This paper presents a robust maximum power point tracking (MPPT) control scheme for a grid-connected permanent magnet synchronous generator based wind turbine (PMSG-WT) using perturbation observation based nonlinear adaptive control. In the proposed control scheme, system nonlinearities, parameter uncertainties, and external disturbances of the PMSG-WT are represented as a lumped perturbation term, which is estimated by a high-gain perturbation observer. The estimate of the lumped perturbation is employed to compensate the actual perturbation and further achieve adaptive feedback linearizing control of the original nonlinear system, without requiring the detailed system model and full state measurements. The effectiveness of the proposed control scheme is verified through both simulation studies and experimental tests. The results show that, compared with the conventional vector controller and the standard feedback linearizing controller, the proposed control strategy provides higher power conversion efficiency and has better dynamic performances and robustness against parameter uncertainties and external disturbances.