In the case of strong coupling and high-precision control, the traditional voltage and current double closed-loop control VSG-based inverters suffer from slow dynamic response and poor anti-interference capability as connected to the grid. Regarding this issue, a new voltage and current dual closed-loop control strategy based on VSG is proposed. Voltage outer loop control is composed of two parts, the linear self-turbulence control that has strong anti-interference ability and speeds up the dynamic response of the VSG-based inverter to the grid and repetitive control improving the tracking accuracy of the dual closed-loop control. The current inner loop is still controlled by PI. . Initially, the mathematical model of VSG-based inverter grid-connected system was analysed in detail. Additionally, the design of linear self-anti-disturbance control and repetitive control were carried out. Finally, the simulation model was built under MATLAB/Simulink platform. The simulation results show that the proposed control strategy accelerates the dynamic response speed of VSG-based inverter grid-connected under power disturbance and three-phase short-circuit fault condition and has strong anti-disturbance capability and high tracking accuracy. The effectiveness and feasibility of the proposed strategy are verified.