TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Material: The particle size of lithium transition-metal complex oxide at accumulation frequency of 90%, is 20 microns or less. The size of secondary particle obtained by aggregating primary particles of lithium transition-metal complex oxide at accumulation frequency of 90%, is 20 microns or less. The primary-particle distribution (R) expressed with the ratio of average particle diameter of primary particle and secondary particle, along center portion of complex oxide, is 0.8-1.2. The lithium transition-metal complex oxide has tap density of 1.75-1.85 g/cm3, specific surface area of 0.6-1.4 m2/g, preferably 0.95-1.05 m2/g, and primary average particle diameter of 0.1-5 microns, preferably 0.5-3 microns. The tap density is the packing density after 200 times tap in a measuring container. The discharge capacitance of a test battery containing anode containing lithium transition-metal complex oxide as anode active material, counter electrode containing lithium metal and reference pole, and a non-aqueous electrolyte, is 8 mAh/g or more at -30degreesC. The lithium transition-metal complex oxide is baked in an air atmosphere.Preferred Properties: The lithium secondary battery has output energy density of 200-500 W/kg, at 50% discharge depth and at -30degreesC. The electrode density of the anode is 2.5-2.7 g/cm3. The cathode contains an amorphous carbon and has open-circuit voltage of 3.6-3.9 V at the time of 50% of charge state.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Materials: The electrolyte contains a mixed solvent of ethylene carbonate, diethyl carbonate and dimethyl carbonate at a volume ratio of 1:1:1. EXAMPLE - Manganese dioxide, cobalt oxide and nickel oxide raw material were mixed with lithium carbonate such that the volume ratio of nickel, manganese and cobalt was 4:3:3. Wet grinding was performed. 2 wt.% polyvinyl alcohol solution was added and mixed for 1 hour. Granulation was performed followed by drying, to obtain particle of size 5-100 microns. The obtained particle was baked in air atmosphere at 1000degreesC for 3-10 hours, followed by pulverization. Coarse particles were removed, to obtain an anode material having layered crystalline structure and particle size of 50 microns or more. The obtained anode active material had tap density of 2.5 g/cm3 and BET specific surface area of 0.6 m2/g. Using the obtained anode material, a lithium secondary battery having excellent charging-discharging characteristics, was obtained.