Abstract: To address the limited capability of existing fractional-order virtual synchronous generators (FOVSGs) to suppress transient overshoot and their insufficient degrees of freedom for parameter tuning in the dynamic response of grid-connected active power and output frequency (hereinafter referred to as power-frequency response), a transient-damping-enhanced fractional-order virtual synchronous generator (TDE-FOVSG) grid-connected control strategy is proposed. First, the influence of fractional-order virtual inertia on the power-frequency dynamic characteristics of the FOVSG is analyzed. Then, a fractional-order differential feedforward compensation link based on angular frequency is introduced into the forward path of the FOVSG active-power loop. By increasing the control degrees of freedom and reshaping the pole-zero distribution, the proposed strategy enhances the transient damping of the system. The controller parameters are determined by combining the Matignon stability criterion, pole-zero distribution, and Bode analysis. Finally, simulations and hardware experiments are conducted under two typical disturbance conditions, namely an active-power reference step and a grid-frequency step. The results show that the proposed strategy can further reduce the transient overshoot of the grid-connected active power of the FOVSG and accelerate the power-frequency dynamic response while preserving the steady-state characteristics of the grid-connected active power, thereby improving the overall power-frequency dynamic performance of the grid-connected FOVSG system.