Highly proten-conductive elastic composites have been successfully prepared from $H_3PO_4$-doped silica gel and styrene-ethylene-butylene-styrene block elastic copolymer. In addition solid state electric double-layer capacitors have been fabricated using the composite as an electrolyte and activated carbon powders(ACP) hybridized with the composite as a polrizable electrode. The cyclic voltammogram of the electric double-layer capacitor fabricated demonstrated that electric charge was stored in the elecric double-layer at the interface between the polarizable electrode and the electrolyte. The value of capacitance of the capacitor was 10 F/(gram of total ACP), which was comparable to that of the capacitors using conventional liquid electrolytes.