NOVELTY - A non-aqueous secondary battery comprises an anode, a cathode, a separator and a non-aqueous electrolyte containing lithium salt. The battery has a thickness of less than 12 mm in flat shape, an energy capacity of 30 Wh or more and a volume energy of 180 Wh/l or more. The anode comprises an active material of composition containing a lithium-nickel-manganese complex oxide. The active material of the cathode comprises double-structure graphite particles.    USE - Used as a non-aqueous secondary battery, such as a lithium secondary battery for electrical storage systems, such as domestic electrical storage systems, solar power generators and electric vehicles.    ADVANTAGE - The non-aqueous secondary battery has high energy capacity and volume energy density, good lifetime and safety, and is inexpensive. The battery has good charging and discharging capacity.    DETAILED DESCRIPTION - The non-aqueous secondary battery has an anode, a cathode, a separator and a structure which accommodates a non-aqueous electrolyte containing lithium salt in a battery container (2). The battery has a thickness of less than 12 mm in flat shape, an energy capacity of 30 Wh or more and a volume energy of 180 Wh/l or more. The anode has an active material of composition containing lithium-nickel-manganese complex oxide expressed by: LiaNibMncMdO2, where M is element(s) chosen from cobalt, aluminum and iron, a is 1-1.1, b and c greater than or equal to 0.3 and less than 0.5, d less than or equal to 0.4, b greater than or equal to c, and b+c+d is 1. The battery contains an electroconductive material which is natural graphite having a specific surface area by the Brunauer Emmett Teller (BET) method of more than 100 m2/g. The active material of the cathode comprises double-structured graphite particles obtained by coating natural graphite particles with amorphous carbon core portion surfaces. The face distance (d002) of the (002) surface according to X-ray wide angle diffraction of the natural graphite is 0.34 nm or less. The natural graphite has an average particle diameter of 15-40 microns and a tap density of more than 0.8 g/cm3. The face distance of the amorphous carbon is more than 0.34 nm. The lithium occlusion amount of the cathode active material at the time of full charge per 1 g of the cathode active material is 220-270 mAh. The solvent of the non-aqueous electrolyte contains ethyl methyl carbonate, ethylene carbonate and vinylene carbonate. The content of vinylene carbonate is 0.1-5 wt.% w.r.t the total solvent weight. The separator is a non-woven fabric and/or paper having a thickness of 20-40 microns and an air permeability of 20-200 second/100 cc.    An INDEPENDENT CLAIM is included for constant current charging of the above non-aqueous secondary battery.    DESCRIPTION OF DRAWING(S) - The figure shows a top and a side view of a non-aqueous secondary battery.    upper cover (1)    container (2)    anode terminal (3)    cathode terminal (4)    injecting nozzle (5)