In this paper, a virtual synchronous generation (VSG) strategy is proposed for a three-phase quasi-impedance source inverter (qZSI). The main objective of the scheme is to provide inertia and damping to the inverter operation in order to add those characteristics to the system in the form of ancillary services, thus contributing a more stable operation of the microgrid where the inverter is operating. The generated references are received by linear control loops on the dc and ac sides of the three-phase qZSI. In the development of this work, the theoretical foundations of the proposal are shown. Also, to prove that the strategy helps to improve the response of the system, simulated results of the qZSI connected to a weak grid are displayed, showing data of the inverter operating in a traditional form (without inertia) and as a VSG, to make comparisons.