A VSG(virtual synchronous generator，VSG) control strategy based on linear quadratic optimal regulator is proposed to solve the problem of frequency fluctuation and frequency offset caused by sudden change of power dispatching instructions under the control of virtual synchronous generator. By analyzing the dynamic response characteristics of the output frequency, the state equation with angular frequency offset and power angle offset as state vectors and input active power deviation as control vectors are established. The optimal control law of the system is solved and the linear quadratic optimal regulator is designed. Model simulation is built in Matlab/Simulink. The simulation results show that the VSG control strategy based on linear quadratic optimal regulator can effectively reduce frequency overshoot and transient response time and improve frequency dynamic response characteristics under load disturbance or active step conditions. In the offgrid mode, the transient stability of the system is good, that is to say, the frequency can be restored to the rated value after a large disturbance, and the operation stability of the system can be improved.