The technology of virtual synchronous generator improves the limitations of inverter control strategy and enhances the acceptance of new energy generation in traditional power system, and yet it greatly affects the frequency dynamic regulation ability of the power grid. Meanwhile, in order to solve the problem of power coupling in medium and low voltage microgrid, many methods have been proposed to change the equivalent output impedance of the system by introducing virtual impedance to improve the stability of microgrid system. For this purpose of optimizing the frequency regulation ability of the system, this paper designs an adaptive control strategy of the moment of inertia and damping coefficient to improve the frequency response characteristics of virtual synchronous generator under the conditions of given active power change and grid frequency fluctuation. In addition, in order to solve the contradiction between the moment of inertia, damping coefficient and the frequency response speed, the voltage vector relationship of virtual synchronous generator under interference is analyzed from the perspective of virtual impedance, and an adaptive virtual impedance control strategy is proposed to accelerate the frequency modulation process of the system. Consequently, one cooperative adaptive control strategy of the moment of inertia, damping coefficient and virtual impedance is proposed. On the basis of ensuring the virtual synchronous generator to give full play to its own operation advantages, this method achieves the purpose of enhancing inertia and accelerating the frequency response speed from various perspectives. The simulation results prove the feasibility of the proposed control strategy.