This paper introduces a new topology of three-level quasi-switched boost F-type inverter (3L-qSBFTI) to improve voltage gain compared to traditional impedance-source inverters (ISIs). This topology uses a switched-capacitor (SC) structure to increase the boost factor to twice that of traditional ISIs. Unlike any conventional SC circuit, the current through capacitors when they are connected in parallel is limited by inductor current. Hence, there is no inrush current through capacitors and semiconductor devices in this operating state. Furthermore, this SC structure helps to obtain self-balanced neutral-point-voltage. The lower-shoot-through (LST) state, which is inserted into P-type small vectors, is used to boost the DC-link voltage. This insertion helps to increase modulation index utilization. As a result, the component voltage rating of the introduced inverter is significantly improved. The comparison study, simulation, and experimental validations have been presented to verify the proposed inverter.