In this paper, we have studied about minimizing the Energy Storage System (ESS) capacity for mitigating the fluctuation of Wind Turbine Generation System (WTGS) by using Electric Double Layer Capacitor (EDLC) and Battery Energy Storage System (BESS). In this case, they have some different characteristics: The EDLC has the ability of generating the output power at high frequency. Thus, it is able to reduce the fluctuation of WTGS in spite of high cost. The BESS, by using Li-Ion battery, takes the advantage of high energy density, however it is limited to use at low frequency response. To verify the effectiveness of the proposed method, simulations are carried out with the actual data of 2MW WTGS in case of worst fluctuation of WTGS is happened. By comparing simulation results, this method shows the excellent performance. Therefore, it is very useful for understanding and minimizing the ESS capacity for mitigating the fluctuation of WTGS.