Removal of the transformer from quasi-Z-source inverters (q-ZSI) in photovoltaic systems creates an oscillating common-mode voltage (CMV) on the parasitic capacitors. Fluctuations in this voltage cause leakage current to flow in the system. Due to the shoot-through (ST) state in q-ZSIs, the CMV fluctuations are also higher than those of the conventional voltage source converters. In this paper, the predictive control method and the concept of virtual voltage vectors (VVVs) and their combination with the odd PWM (OPWM) method are proposed for elimination of the oscillation of the common state voltage in the q-ZSI. In the proposed method, the CMV fluctuations are kept constant for a complete switching period. In addition, the total harmonic distortion (THD) of the output current of the converter decreases, and consequently, the converter's operating range and performance increase. By simulating a two-level q-ZSI, the performance of the proposed method are proved.