This paper proposes a new matrix converter topology, which is a combination of Quasi-Z network and single-phase matrix converter. The proposed single-phase Quasi-Z-Source matrix converter can provide a wide range of output AC voltages in buck-boost mode, it can also allow short circuit and open circuit simultaneously. So the device requirements are reduced greatly and thus can help to improve system reliability. What’s more the output waveforms are obtained with a step-changed frequency and a variable amplitude. Firstly, the operation principle and running mode of single-phase Quasi-Z-Source matrix converter are analyzed. On the basic of the converter’s circuit equations, the voltage gain G of the proposed converter is derived. To verify the performance of the converter, the PSIM software has been used and the simulation results verified the proposed theoretical analysis.