Abstract: Virtual synchronous generator（VSG） has the problems of the output active power transient oscillation and steady-state deviation under active power command and grid frequency disturbance. Adding the transient damping link in the control can suppress the oscillation and avoid the steady-state deviation, but there is a high overshoot problem. By establishing the active closed-loop small signal model of VSG under two disturbances, the oscillation suppression effect is analyzed according to the root locus. Furthermore, combined with the zero point analysis of overshoot, the causes and characteristics of VSG overshoot with transient damping strategy are obtained, and two VSG power oscillation suppression strategies based on active power transient compensation are proposed, i.e., transient feedforward compensation and transient feedback compensation. Both the two improved strategies can improve the transient damping of the system and effectively suppress the VSG active power oscillation, which will not increase the steady-state deviation and can greatly reduce the overshoot. The correctness and effectiveness of the proposed strategy are verified by MATLAB/Simulink simulation and StarSim hardware-in-the-loop experiment.