With the increase of installed capacity of photovoltaic power generation, the distributed photovoltaic power grid with traditional grid-connected control strategy would greatly reduce the inertia of power grid and undermine the stability of power grid.Given the advantages of quasi-Z-source inverter, this paper presents a Virtual Synchronous Generator (VSG) grid-connected control scheme based on energy-storaged quasi-Z-source inverter to solve the problem, in which the energy storage unit is inserted.Firstly, this paper analyzes the working mode of the energy-storaged quasi-Z-source. Then the VSG technology is used to control the output power of the system, and the PV power is clamped at the maximum power point by regulating the shoot-through duty ratio so that the battery automatically compensates for the power shortage. In addition, this paper discusses the problem of the battery configuration considering the transient response of VSG, and deduces the relationship between shoot-through duty ratio and moment of inertia as well as damping coefficient of VSG, which provides criterion for the parameter design of quasi-Z-source inverter with VSG control. The simulation and experiment results verify the effectiveness of the method proposed in this paper. This work is supported by National Natural Science Foundation of China (No. 51407122).