NOVELTY - A lithium secondary battery consists of a cathode (2), an anode (1), and a separator (3). The separator consists of a microporous membrane having porous layers (I,II). Layer (I) contains a thermoplastic resin, and layer (II) contains a filler having an allowable temperature limit of 150 degrees C or more. Porous layer (I) faces the cathode. The primary particle diameter of the anode active material and cathode active material is 1 mu m or less. The thickness of anode-mix layer and cathode-mix layer is 50 mu m or less.    USE - Lithium secondary battery. Uses include but are not limited to mobile telephones, notebook personal computers, hybrid vehicles, and electric bikes.    ADVANTAGE - The lithium secondary battery has excellent economical efficiency, safety even in high-temperature environment, reliability with respect to short circuit, and charging-and-discharging characteristics even during abnormal overheating. The separator has excellent dimensional stability at high temperatures. The lithium-titanium complex oxide has excellent thermal stability, and does not produce lithium dendrite.    DETAILED DESCRIPTION - A lithium secondary battery consists of a cathode having a cathode-mix layer which contains lithium-titanium complex oxide as cathode active material, an anode having an anode-mix layer containing anode active material, and a separator. The lithium-titanium complex oxide has spinel-type crystal structure or ramsdellite-type crystal structure. The separator consists of a microporous membrane having porous layers (I,II). Layer (I) contains a thermoplastic resin, and layer (II) contains a filler having an allowable temperature limit of 150 degrees C or more. Porous layer (I) faces the cathode. The primary particle diameter of the anode active material and cathode active material is 1 mu m or less. The thickness of anode-mix layer and cathode-mix layer is 50 mu m or less.    DESCRIPTION OF DRAWING(S) - The drawing shows a top view and a sectional view of the lithium secondary battery.    Anode (1)    Cathode (2)    Separator (3)    Armored can (4)    Insulator (5)