The virtual synchronous generator (VSG) control strategy is widely used in distributed power supplies for the stable operation. In order to meet the needs of grid-connected and island dual-mode operation, a self-adaptive dual-mode operation control strategy based on VSG is proposed in this paper. Firstly, the dual-mode operation control strategy of VSG is given, that is, the current-controlled VSG is adopted in grid-connected mode and the voltage-controlled VSG is adopted in island mode. In order to realize seamless switching, a new slow start control strategy is proposed in switching from grid-connected mode to island mode. Then, to solve the overload problem caused by VSG control in grid-connected operation, a current-controlled VSG with self-adaptive droop-damping coefficient and reactive power droop coefficient is proposed. Finally, the proposed control strategy is verified effectively by simulation on the energy-stored quasi-Z-source inverter micro-grid system.