An electric double-layer capacitor is provided which is larger in electrostatic capacitance, and can be much higher in rated voltage, than that in the prior art using a liquid electrolyte solely composed of an ionic liquid. Having an electrolyte and electrodes, the capacitor incorporates an atom encapsulated fullerene or an atom encapsulated fullerene salt in the electrolyte. The electrolyte can either be a liquid solution or a solid. With the electrolyte being a solid, cations of the atom encapsulated fullerene or atom encapsulated fullerene salt may either be made movable or static in the electrolyte.