NOVELTY - The power supply system (1) comprises battery module (A) which supplies electric energy to the outside, and battery module (B) which supplies electric energy to module (A). Module (A) comprises a non-aqueous electrolyte battery comprising an anode and a cathode containing a carbonaceous material. Module (B) comprises a battery comprising a cathode containing an active material having preset lithium-ion absorbing potential, and an anode containing lithium metallic oxide. Module (B) is chargeable in a range of 20-80% of charging depth.    USE - Power supply system is used for motor cars (claimed). Can also be used for hybrid vehicles, motor cycles, electric trams, and wind-power plants.    ADVANTAGE - The power supply system has excellent cycle performance in fast charging. The power supply system can be efficiently charged during regenerative charging, and also discharged for a prolonged period when a motor car runs. Degradation due to dissolution/deterioration of cathode current collector, which is noticeable in an over-discharge cycle in a high-temperature cycle, is prevented, and increase in electrode resistance is suppressed. The reaction of lithium complex oxide with non-aqueous electrolyte is suppressed.    DETAILED DESCRIPTION - The power supply system (1) comprises battery module (A) which supplies electric energy to the outside, and battery module (B) which supplies electric energy to module (A). Module (A) comprises a non-aqueous electrolyte battery comprising an anode and a cathode containing a carbonaceous material. Module (B) comprises a non-aqueous electrolyte battery comprising a cathode containing an active material having lithium-ion absorbing potential of 0.4 V (vs. lithium/lithium ion) or more and an average particle diameter of 1 mu m or less, and an anode containing lithium metallic oxide. Module (B) is chargeable in a range of 20-80% of charging depth so that a charging current density (A/kg) of the battery becomes higher than that of battery of module (A). The lithium metallic oxide is of formula: LixCoyM1-yO2.    M=nickel, manganese, aluminum and/or tin;    x=greater than 0 and 1.1 or less;and    y=0 or more, and less than 1.    Preferably, the lithium metallic oxide is of formula: LixCoyNizMn1-y-zO2.    x=greater than 0 and 1.1 or less;    y=0.1-0.6;and    z=0.1-0.8.    The anode of battery of module (B) further includes lithium-manganese complex oxide having spinel structure, and lithium-manganese-nickel complex oxide having spinel structure, and lithium metal phosphate having olivine structure.    DESCRIPTION OF DRAWING(S) - The drawing shows the block diagram of the power supply system and motor car.