Virtual synchronous generator (VSG) faces the problem of the output active power oscillation under active power command and grid frequency disturbance under grid-connected operation. In view of this, an improved VSG control strategy based on transient damping enhancement is proposed. First, based on state feedback theory, the physical meaning of the proposed control method is analyzed, and the system transient damping is enhanced by adding high-frequency components of angular frequency and electromagnetic power to the conventional VSG active power control loop. Second, based on the proposed control method, a closed-loop small signal model of the active power control loop is established, and the system characteristic root locus is used to analyze the impact of the proposed control method on VSG active power oscillation suppression. Design guidelines of various state feedback parameters are also provided to guide feedback coefficient design. The proposed control method can effectively suppress VSG output active power oscillations caused by sudden changes in active power commands and grid frequency, without affecting the system's steady-state characteristics. Finally, the simulation and experimental results demonstrate that the proposed method has better active power oscillation suppression performance, eliminates steady-state deviation, and can be applicable to different grid strengths.