TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The doped quantity of the lithium ions in the composite porous material is 1050-2050 mAh/g or less. The negative electrode active material is a composite porous material obtained by adhering 10-60 wt.% carbon material on the surface of activated carbon and having diameter of 20 Angstrom or more computed by Barrett-Joyner-Halenda (BJH) method, mesopore amount (V1) derived from pore with diameter of 500 Angstrom or less of 0.01-0.25 cc/g and micropore amount (V2) derived from pore with diameter of less than 20 Angstrom of 0.001-0.2 cc/g. The positive electrode active material is a composite porous material obtained by adhering 10-60 wt.% carbon material on the surface of activated carbon having BET specific surface area of 1500-3000 m2/g, with diameter of 20 Angstrom or more computed by Barrett-Joyner-Halenda (BJH) method, and mesopore amount (V1) derived from pore with diameter of 500 Angstrom or less of 0.3-0.8 cc/g and micropore amount (V2) derived from pore with diameter of less than 20 Angstrom of 0.5-1 cc/g, or obtained by adhering carbon material on the surface of activated carbon having BET specific surface area of 3000-4000 m2/g, with diameter of 20 Angstrom or more computed by Barrett-Joyner-Halenda (BJH) method, mesopore amount (V1) derived from pore with diameter of 500 Angstrom or less of 0.8-1.25 cc/g and micropore amount (V2) derived from pore with diameter of less than 20 Angstrom of 0.8-3 cc/g. Preferred Properties: The thickness of negative electrode active material layer is 20-45 mu m or more per single surface. The lattice spacing of (002) plane of the negative electrode active material, which is a hard carbon is 0.349 nm or more.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The lactone compound is ( gamma )-butyrolactone, ( beta )-butyrolactone, or beta -propiolactone. The nonaqueous electrolyte solution further contains compound chosen from vinylene carbonate and 1,3-propanesultone.