The article proposes a novel topology of three-level quasi-Z-source active neutral point clamped (qZS-ANPC) inverter that connects the dc power supply to an active neutral point clamped (ANPC) three-level inverter through an intermediate network. Besides the buck-boost function, this topology also provides the potential for fault tolerance. It has great importance for the safety and dependability of the system in practical industrial applications. In this context, the article studies some fault-tolerant strategies of the proposed qZS-ANPC inverter under Sa1, Sa2, or Sa5 open-circuit fault. The relevant fault-tolerant strategy is designed for each device fault, including reconstructing the topology, changing the modulation signals, and adjusting the values of shoot-through duty cycle and modulation index. This enables the inverter to operate continuously under open-circuit fault conditions, substantially improving the reliability and robustness of the system. Moreover, the proposed solution does not add extra components to the three-level qZS-ANPC inverter, which has low robust operating cost and is convenient for engineering implementation. Finally, the validity of proposed strategies and high reliability of this inverter topology are confirmed by simulations.