To address the problems of quasi-Z-source inverters with limited boosting ability and high voltage stress, a novel class of multicell switched-inductor quasi-Z-source inverters is proposed. The new inverter is based on the quasi-Z-source inverter in which the inductors in the impedance source network are replaced by a multicell switched-inductors. In this paper, a detailed description of the topology and operating principle of the new inverter is first made. Then, a deep comparison of the proposed topology with the existing topologies is performed by selecting the appropriate number of switched-inductor units. Finally, to verify the feasibility and superiority of the proposed new topology, a great number of simulations and experiments are conducted. The results demonstrate that, compared to the original quasi-Z-source inverter and existing modified topologies, the boosting capacity of the proposed new inverter increases significantly with the number of cascaded switched-inductor units, and its voltage stress across the capacitors and current ripple through the inductors are effectively reduced.