Solid state electric double-layer capacitors have been fabricated using a composite composed of H3PO4-doped silica gel and styrene-ethylene-butylene-styrene elastomer as the electrolyte. A composite hybridized with activated carbon powders (ACP) was the polarizable electrode. The cyclic voltammogram of the electric double-layer capacitor fabricated demonstrated that electric charge was stored in the electric double-layer at the interface between the polarizable electrode and the electrolyte. Resistance of the capacitor obtained from impedance plots in ambient air was smaller by three orders of magnitude than that of the capacitor in a dry Ar atmosphere. The drastic decrease in the resistance should be ascribed to the increase in the proton conductivity of the composite due to the water adsorption in H3PO4-doped silica gel in an ambient atmosphere. The value of capacitance of the capacitor in an ambient atmosphere was 10 F/(gram of total ACP), which was 10 times larger than that of the capacitor in a dry Ar atmosphere. The large capacitance of the capacitor in an ambient atmosphere is attributable to the formation of electric double-layer with large electric charge at the interface between the composite and ACP in the capacitor due to the water adsorption.