Due to the high-performance requirements of power converters in industrial applications, sliding-mode control has drawn extensive research attention for its insensitivity against external disturbances. In order to ensure this advantage while suppressing the chattering problem caused by discontinuous switching functions, in this article, a fuzzy sliding-mode control (FSMC) strategy consisting of three control loops is proposed for three-phase three-level neutral-point-clamped active front-end rectifiers. In the power tracking loop, an improved super-twisting algorithm is proposed to enforce the tracking errors of active power and reactive power to bounded regions in finite time and guarantee the transient performance. Next, in the dc-link voltage regulation loop, the regulation error of dc-link voltage converges to a bounded region with a super-twisting extended state observer-based FSMC strategy. A simple but efficient proportional-integral controller is employed in dc-link voltage balancing loop to reduce the voltage difference between two dc-link capacitors. The proposed controller is characterized by attenuated chattering phenomenon and improved the dc-link voltage regulation performance, disturbance rejection ability, and power tracking performance. Experimental results are provided to verify the effectiveness and superiority of the proposed strategy.