TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Compositions: Lithium salt is lithium hexafluorophosphate (LiPF6). Negative active material is an active material formed by doping lithium ions to composite porous material and depositing carbonaceous material on the surface of activated carbon, mass ratio of activated carbon of carbonaceous material is 10-60 mass%, thickness of negative electrode active layer is 20-45 mu m per single side, and doped quantity of lithium ion with respect to composite porous material is 1050-2050 mAh/g per unit mass of composite porous material. Preferred Parameters: Negative electrode active material is a composite porous material which adheres carbon material on the surface of activated carbon and satisfies equations Vm1=0.01-0.25, Vm2=0.001-0.2, and Vm1/Vm2=1.5-20, where Vm1 is the mesopore volume (cc/g) of pores with diameter of 20-500 Angstrom calculated by Barrett-Joyner-Halenda (BJH) method, and Vm2 is the micropore volume (cc/g) of pores with diameter of less than or equal to 20 Angstrom calculated by micropore size distribution (MP) method. Lattice spacing of (002) plane of the negative electrode active material, which is a hard carbon, is greater than or equal to 0.349 nm. Positive electrode active material satisfies equations V1=0.3-0.8 and V2=0.5-1, where V1 is the mesopore volume (cc/g) of pores with diameter of 20-500 Angstrom calculated by BJH method, and V2 is the micropore volume of pores with diameter of less than or equal to 20 Angstrom calculated by MP method, and Brunauer-Emmett-Teller (BET) specific surface area of positive electrode active material, which is activated carbon, is 1500-3000 m2/g. Positive electrode active material satisfies equations V1=0.8-2.5 and V2=0.8-3, BET specific surface area of positive electrode active material, which is activated carbon, is 3000-4000 m2/g.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: Non-aqueous electrolyte solution further contains non-cyclic fluorine-containing ether of formula R1-O-R2 (2), cyclic carbonate, vinylene carbonate, and/or fluorine-containing gamma -butyrolactone.R1, R2=2-6C fluorinated alkyl. Preferred Definitions:    X1-X6=halo, alkoxy, or aryloxy.