TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The positive electrode contains positive electrode active material, electroconductive auxiliary material, and binder. The negative electrode contains negative electrode active material, electroconductive auxiliary material, and binder. Although both positive electrode active material and negative electrode active material consist of lithium-transition metal composite oxide in which insertion and desorption are possible, both active materials are different from each other. The positive electrode active material consists of lithium-transition metal composite oxide containing transition metal element(s) chosen from cobalt, nickel, manganese, chromium, vanadium, titanium and iron, preferably lithium iron phosphate. The negative electrode active material consists of lithium-transition metal composite oxide containing transition metal element(s) chosen from vanadium, titanium and iron, preferably lithium-titanium-phosphate. The electroconductive auxiliary material is chosen from carbon black, Ketchen Black (RTM: electroconductive black), acetylene black, a carbon whisker, carbon fiber, natural graphite, artificial graphite, carbon nanoparticles, carbon nanotubes, titanium oxide, ruthenium oxide, aluminum and/or nickel, preferably acetylene black. The solid electrolyte salt is lithium nitrate, lithium hydroxide, lithium fluoride, lithium chloride, lithium bromide, lithium iodide, lithium perchlorate, lithium sulfate, lithium acetate, lithium tetrafluoroborate, lithium hexafluorophosphate, lithium bis(trifluoromethanesulfonyl)imide, lithium bis(pentafluoroethanesufonyl)imide, lithium oxide and/or lithium carbonate, preferably lithium perchlorate or lithium sulfate.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The nonaqueous solvent is N,N-dimethylformamide, dimethylsulfoxide, N,N-dimethylacetamide, 1,3-dimethyl-2-imidazolidinone, N-methyl-2-pyrrolidone, tetrahydrofuran, methanol, ethanol, n-propanol, isopropanol, 1,2-diethoxy ethane, ethyl acetate, butyl acetate, methoxybutyl acetate, methyl-cellosolve acetate, ethyl cellosolve acetate, propylene-glycol-monomethyl-ether acetate, diethyl carbonate, diethyl carbonate, ethylene carbonate, propylene carbonate and/or acetonitrile. The nonaqueous solvent is N-methyl-2-pyrrolidone.    TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The gel-like solid electrolyte further contains water-soluble polymer. The water-soluble polymer is gelatin, polyvinyl alcohol, polyvinylpyrrolidone, starch, cellulose or its derivative(s), polyethylene oxide, polysaccharide, polyvinylamine, chitosan, polylysine, polyacrylic acid, polyalginic acid, poly hyaluronic acid and/or carboxy cellulose, and non-aqueous solvent. The water-soluble polymer is polyvinyl alcohol. The binder is polyethylene, polypropylene, polytetrafluoroethylene, polyvinylidene fluoride, styrene-butadiene rubber, fluororubber, tetrafluoroethylene-hexafluoroethylene copolymer, tetrafluoroethylene- hexafluoropropylene copolymer, tetrafluoroethylene-perfluoroalkyl vinyl ether copolymer, fluorinated vinylidene-hexafluoropropylene copolymer, fluorination vinylidene- chlorotrifluoroethylene copolymer, the ethylene-tetrafluoroethylene copolymer, polychlorotrifluoroethylene, fluorinated vinylidene-pentafluoropropylene copolymer, propylene-tetrafluoroethylene copolymer, ethylene-chlorotrifluoroethylene copolymer, fluorinated vinylidene-hexafluoropropylene tetrafluoroethylene copolymer, fluorination vinylidene-perfluoromethyl-vinylether-tetrafluoroethylene copolymer and/or ethylene-acryl acid copolymer, preferably polytetrafluoroethylene.