A non-aqueous electrolyte secondary cell which achieves satisfactory low temperature characteristics and high safety against overcharging in combination. The cell includes a lithium-containing cathode, an anode capable of doping and undoping lithium, a non-aqueous electrolyte and a separator. The separator is made up by a plurality of layers of a porous material or materials presenting micro-sized pores. The layers of the porous material or materials is formed of micro-porous separator materials representing different combinations of the porosity, melting point or material/compositions.