The traditional virtual synchronous generator (VSG) control strategy provides virtual damping and inertia in the grid-connected operation of the inverter, which increases the frequency and voltage support capability of the system. However, the introduced virtual inertia increases the order of the system, which will cause the output of the active power to oscillate during the grid-connected operation of the inverter; the introduced virtual inertia and damping make the response speed of the system slower. Based on the analysis of frequency domain characteristics of fractional virtual inertia link, a virtual synchronous generator control method with fractional virtual inertia is proposed. Compared with the traditional VSG technology based on the first order inertia element, the VSG control with fractional virtual inertia increases the adjustable parameters, significantly suppresses the oscillation of the active power, and improves the performance of the grid-connected inverters. Simulation results verify the feasibility and superiority of the proposed control strategy.