In this paper, the control of a PMSG (permanent magnet synchronous generator)-based variable-speed wind turbine system with a back-to-back converter is considered. The uncertainty and disturbance estimator (UDE)-based control approach is applied to the regulation of the DC-link voltage and the control of the RSC (rotor-side converter) and the GSC (grid-side converter). For the rotor-side controller, the UDE-based vector control is developed for the RSC with PMSG control to facilitate the application of the MPPT (maximum power point tracking) algorithm for the maximum wind energy capture. For the grid-side controller, the UDE-based vector control is developed to control the GSC with the power reference generated by a UDE-based DC-link voltage controller. Compared with the conventional vector control, the UDE-based vector control can achieve reliable current decoupling control with fast response. Moreover, the UDE-based DC-link voltage regulation can achieve stable DC-link voltage under model uncertainties and external disturbances, e.g. wind speed variations. The effectiveness of the proposed UDE-based control approach is demonstrated through extensive simulation studies in the presence of coupled dynamics, model uncertainties and external disturbances under varying wind speeds. The UDE-based control is able to generate more energy, e.g. by 5% for the wind profile tested.