In this article, a two-stage control scheme consisting of an adaptive-gain second-order sliding mode (SOSM) controller and a switched high-gain observer (HGO) is proposed for the three-level neutral-point-clamped (NPC) converter. The adaptive-gain SOSM control method is applied both in the voltage regulation loop and instantaneous power tracking loop, thus, the boundary of the disturbance derivative does not need to be known a priori. Compared with the fixed-gain SOSM, it provides a faster dynamic and a better steady-state response for the NPC converter. On the other hand, the conventional disturbance compensation observer used in the power system suffers from the adverse effects of measurement noise, which limits the performance of the observer. A switched HGO is combined with the adaptive-gain SOSM controller in the voltage regulation loop to address this issue. By using a switched observer gain, the switched HGO greatly diminishes the performance degradation induced by the inevitable measurement noise. Finally, several experiments between the representative extended state observer-based SOSM control scheme and the proposed control method are carried out for a comparison. The results demonstrate the feasibility and effectiveness of the proposed approach.