In this paper, an operation scheme for a single-phase grid-connected quasi-impedance source inverter (qZSI) is proposed. The proposal indicates that, to achieve a more stable operation for the microgrids, the qZSI must emulate the inertia of a real synchronous machine (SM) through a virtual synchronous generation (VSG) strategy. The proposed VSG strategy generates the setpoints for the ac and dc sides of the converter. These references are taken by a direct model-based predictive control (MPC) scheme that is responsible for controlling the variables on both sides of the inverter. For implementing the MPC scheme, the model of the qZSI will allow predicting the variables that must be controlled. Simulations are shown to demonstrate the feasibility of this proposal. In the simulations a desirable performance of the converter will be observed, controlling the power injection to a single-phase grid as if this converter were an SM.