The hybrid active neutral-point-clamped(HANPC) three-level inverter(TLI) has the advantage of high efficiency and low cost due to the partial use of SiC devices. However, the magnitude of AC output voltage cannot exceed that of DC input voltage, which limits its application field. This paper puts forward a novel topology and modulation method of the high-gain HANPC TLI. The proposed topology combines the advantages of reduced count of SiC MOSFETs and single-stage boosting ability. To further improve system efficiency, a novel modulation method is designed, in which the SiC MOSFETs and Si IGBTs are operated in high frequency and fundamental frequency, respectively. To realize the function of voltage boosting without affecting the normal ac output voltage, the upper-shoot-through(UST) and lower-shoot-through(LST) states are inserted within the dwell times of small vectors. Moreover, the neutral point(NP) voltage balance is actively controlled by introducing a distribution factor to regulate duty cycle of redundant small vectors, which improve system reliability. Experimental tests verify the performance of the proposed topology and strategy.