The Z-source inverter can overcome several inherent limitations of conventional inverters, realize buck-boost voltage capability with a single-stage inverter, and improve inverter's safety. However, it needs to be optimized in two aspects: mitigating the constraining effect of the shoot-through duty ratio D and the modulation index M; reduction of the inductance of the magnetic elements and the size of the magnetic core in the Z-Source network. This article presents a new quasi-Z-source inverter (qZSI) that either has a coupled-inductor multiplier voltage rectifier (CMVR) cell or an improved CMVR cell embedded into it. The CMVR qZSIs can implement a boost factor given by k(N)/(1 - kD), k(N) > 1, which mitigates the constraining effect of D and M, as well as enables high voltage boosting with a large value of M. The CMVR qZSI has low weight of the magnetic elements in the CMVR cell due to the use of step-down transformer. The operating principle, voltage relationship between each component, and the comparison in voltage and current stress on components, magnetic elements, has been described. A 1 kW prototype was built in the laboratory to verify the validity of the proposed inverter. Experimental results are in good agreement with the analysis results.