In view of the inverter-side control of the grid simulator, the traditional proportional-integral control has problems such as static difference, delay and oscillation for the tracking of a given voltage. It is proposed that both the current inner loop and the voltage outer loop of the grid simulator inverter side be used QPR control. In this paper, a suitable grid simulator structure is selected, a single-phase inverter mathematical model is established, an LC filter is used, and a QPR double closed-loop controller is designed. Compared with traditional proportional-integral control, the simulation verifies that the quasi-proportional resonance controller can effectively improve the tracking ability of the system to the command voltage and the stability of the output voltage. Based on the controller hardware-in-the-loop test (CHIL) technology, a power grid simulator experimental platform was built and tested to verify the feasibility of the control strategy.