An electric double-layer capacitor (ELDC) of activated carbon electrode is prepared using a proton-conducting hydrogel polymer electrolyte, which is composed of poly(vinyl alcohol), silicotungstic acid, $H_3PO_4$, and deionized water. A solid film by evaporating the hydrogel polymer electrolyte is also prepared for comparison. The hydrogel polymer electrolyte also acts as a separator with the thickness of about $80{mu}m$ and the room-temperature ionic conductivity of $10^{-2}S;cm^{-1}$. The EDLC containing the symmetric electrodes of activated carbon shows the specific capacitance of $58F;g^{-1}$ at $100mV;s^{-1}$ with a good cycle life, implying that the hydrogel polymer electrolyte is very promising for use in EDLCs.