NOVELTY - A non-aqueous-electrolyte secondary battery has a positive electrode (1) having a positive electrode active material that expresses the electric potential of greater than or equal to 4.5 V on a metallic lithium standard, a negative electrode (4), and a non-aqueous electrolyte dissolved in non-aqueous solvent. The non-aqueous electrolyte contains fluorine-containing phosphate ester compounds (A).    USE - Non-aqueous-electrolyte secondary battery i.e. lithium ion secondary battery that is utilized as power supply for a mobile telephone, a notebook personal computer and a tablet computer, and electric vehicles.    ADVANTAGE - The battery has high output density, energy density, charging/discharging cycle life and cycling characteristics, and can suppress the increase of a positive electrode interfacial resistance by using a membrane coat formed on the positive electrode. The battery does not easily decompose the electrolyte solution even when charging/discharging is carried out at a high voltage.    DETAILED DESCRIPTION - A non-aqueous-electrolyte secondary battery has a positive electrode having a positive electrode active material that expresses the electric potential of greater than or equal to 4.5 V on a metallic lithium standard, a negative electrode, and a non-aqueous electrolyte dissolved in non-aqueous solvent. The non-aqueous electrolyte contains fluorine-containing phosphate ester compounds (A) of formulae (R1O-P(=O)(OR2)-OR3) (I) and (II).    R1-R3=1-6C linear or branched alkyl or 1-6C linear or branched fluorine-containing alkyl;    R4=1-6C linear or branched fluorine-containing alkyl;and    Ct=2-6C fluorine-containing alkylene or 2-6C linear or a branched alkylene.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of a non-aqueous-electrolyte secondary battery.    Positive electrode (1)    Positive electrode stainless steel cap (2)    Negative electrode stainless steel cap (3)    Negative electrode (4)    Stainless steel plate spring (5)    Inorganic filler containing polyolefin porous separator (6)    Gasket (7)