In a traditional energy storage virtual synchronous generator (VSG) with grid-connected active power (GCAP) it is difficult to balance the steady-state deviation and dynamic oscillation, because of the coupling of its primary frequency modulation coefficient and virtual damping coefficient. Thus a GCAP dynamic oscillation suppression strategy for an energy storage VSG based on active power feed-forward compensation is proposed. The active power is fed-forward to the GCAP closed control loop through the first-order low-pass filter, and the GCAP dynamic performance for energy storage VSG is optimized by adjusting the feed-forward parameter without using the differential operation. The VSG primary frequency modulation characteristic is not affected. Then a small signal model of GCAP closed-loop for the energy storage VSG based on active power feed-forward compensation is established, and the setting method of the feed-forward coefficient is given. Finally, comparison of simulation and experimental test is used to verify that the proposed strategy can effectively eliminate the steady-state deviation, and dynamic oscillation of GCAP of the energy storage VSG under two-step disturbances of active power command as well as grid frequency, and there is no risk of frequency overshoot.