TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The ratio of number of moles of tungsten occupied with respect to sum total number of moles of tungsten and zirconium is 30-100%. The complex oxide is oxide containing nickel, cobalt and manganese. The positive electrode active material contains secondary particles formed by aggregating two or more primary particles of lithium transition metal oxide. The secondary particles comprise a hollow portion. The positive electrode active material has a through-hole penetrating in the secondary particles, and the hollow portion and the exterior are connected. The positive electrode active material has composition of formula: Li1+mNipCoqMnrM1sWaZrbO2.M1=aluminum, chromium, iron, vanadium, magnesium, titanium, molybdenum, copper, zinc, gallium, indium, tin, lanthanum, cerium, calcium or sodium;m=0-0.2;p=0-0.6 (including 0.6);q,r=0-0.5;s=0-0.02;anda,b=more than 0.The battery further consists of negative mix layer coated on the negative electrode collector. The porosity of the negative mix layer is 0.30 or more, preferably 0.60 or less. A separator is further provided between the positive mix layer and negative mix layer. Preferred Properties: The positive mix layer has porosity of 0.60 or more. The positive mix layer has first peak with pore diameter (D1) of 0.25 mu m or less and second peak with pore diameter (D2) larger than the pore diameter (D1). The pore diameter (D1) originates in the voids between the electroconductive material and the pore diameter (D2) originates between the particles of the positive electrode active material. The pore diameter (D1) is 0.05 or more. The dibutyl phthalate oil absorption amount of the positive electrode active material is 20 ml/100 g or more, and the dibutyl phthalate oil absorption amount of the electroconductive material is 100 ml/100 g or more. The opening width of the through-hole is 0.01-2.0 mu m. The BET specific surface area of the positive electrode active material is 0.5-1.9 m2/g. The average particle diameter of the positive electrode active material is 3-10 mu m. Preferred Process: Aluminum ions are supplied to aqueous solution of transition metal compound containing lithium-transition metal oxide, and particles of transition metal hydroxide are deposited from the aqueous solution by raw water oxide formation process. The transition metal hydroxide and lithium compound are mixed to prepare a non-baked mixture. The mixture is baked to obtain active material particles. The raw water oxide formation process is nucleation process of depositing transition metal hydroxide from the aqueous solution at pH of 12 or more and ammonium ion concentration of 25 g/l or less. The transition metal hydroxide is grown at pH of less than 12. The baking process is performed at temperature (T1) of 800-1000 degrees C or at 700-900 degrees C and further at temperature (T2) of 800-1000 degrees C. The temperature (T2) is higher than calcination temperature (T1).