A carbonaceous material having a pore size distribution, as determined from a nitrogen adsorption isotherm, in which pores with a radius of up to 10 .ANG. account for at most 70% of the total pore volume, and having a specific surface area, as measured by the nitrogen adsorption BET method, of 1-500 m.sup.2 /g is optimized for the penetration of non-aqueous electrolyte solution to the interior thereof and the surface adsorption of ionic molecules so as to form an electrical double layer thereon. Electrical double-layer capacitors assembled using polarizable electrodes made with the carbonaceous material have a high voltage, a high energy density, a high capacitance, a long cycle life, and are amenable to miniaturization.