TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Component: The lithium secondary battery is capable of charging/discharging.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The lithium-transition metal composite oxide contains lithium, and cobalt, nickel, manganese, sodium, magnesium, calcium, strontium, barium, aluminum, germanium, titanium, vanadium, chromium, iron, copper, zirconium, niobium, molybdenum, tungsten, tin, hafnium, or tantalum. The lithium-transition metal composite oxide is of formula: Li1+x(Ni1/3\|(d)1Co1/3\|(d)2Mn1/3\|(d)3)1-xO2 (V), Li1+aMO2 (VI), or Lix3MPO4 (XI), preferably of formula: Li1+a1NixMnyCozO2 (VII), LitMgxNiyMe'zO2 (VIII), Lia2Co1-x1-y1-z1ZrxMgy1M'z1O2 (VIII), LibMnsNit1CouXvO2 (IX), or Li1+s2Nix2Coy2Mnz2Cat2Mgu2Av2O2 (X), and has a laminated structure obtained by laminating lithium layer containing lithium ions, oxygen layer containing oxide ions, and transition metal layer containing nickel, cobalt, and manganese, or super-lattice structure containing P2/c space groups. The mass ratio of lithium-transition metal composite oxide (VIII) with respect to lithium-transition metal composite oxide (IX) is 51:49-90:10. The lithium-transition metal composite oxide (XI) is preferably lithium-iron phosphate. The positive electrode further contains monofluorophosphate, difluorophosphate, or lithium difluorophosphate. The negative electrode contains metallic lithium or lithium-containing alloy containing oxide, nitrided transition metal, or carbon material, in which doping and de-doping of lithium ions is possible.x=-0.1-0.2;d1,d2,d3=0-0.1;M=transition metal element chosen from V, Ti, Cr, Mn, Fe, Co, Ni, or Cu;a=0.05-0.25;x+y+z=1;a1=-0.05-0.25;Me'=Al, Co, or Mn;t=0.8-1.3;x=0.01-0.2;y=0.6-0.98;z=0.01-0.2;M'=Al, Ti, or Sn;a2=0-1.1;x1=0.0001 or more;y1=0.0001 or more;x1+y1+z1=0.03 or less;X=Zr, Mg, Al, Ti, or Sn;b=0-1.1;s=0.1-0.5;t1=0.1-0.5;v=0.0001-0.03;s+t+u+v=1;A=Na, Al, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, or W;s2=-0.05-0.2;x2+y2+z2+t2+u2+v2=1;x2=0.3-0.7;y2=0.1-0.4;z2=0.1-0.4;t2=0.0002-0.01;u2=0-0.005;t2+u2+v2=0.0002-0.02;andx3=0.85-1.15.Preferred Property: The positive electrode has charge upper limit electric potential of 4.2 V or more, preferably 4.3-4.7 V.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The content of additive (A) in the nonaqueous electrolyte is 0.01 %mass or more. The nonaqueous electrolyte further contains 0.01-10 %mass carbonate compound containing carbon-carbon unsaturated bond or fluorophosphoric acid compound containing fluorine atom and cyclic sultone compound as an additive (B), with respect to total amount of electrolyte. The additive (B) is preferably chosen from vinylene carbonate, vinyl ethylene carbonate, fluoroethylene carbonate, difluoroethylene carbonate, lithium monofluorophosphate, lithium difluorophosphate, lithium difluoro(bisoxalato)phosphate, lithium tetrafluoro(oxalate)phosphate, 1,3-propane sultone, and 1,3-propene sultone.