NOVELTY - A non-aqueous-electrolyte lithium ion secondary cell (1) has a positive electrode (2) with a positive electrode compound material containing a positive electrode active material, an electroconductive material, a binder and an activated carbon, a negative electrode (3) having a negative electrode compound material containing a carbon material and a binder, and a non-aqueous electrolyte formed by dissolving an electrolyte in a nonaqueous solvent. The electrolyte contains a lithium salt containing fluorine element and a subsidiary component electrolyte (I).    USE - Non-aqueous-electrolyte lithium ion secondary cell is used for mobile telephone, personal computer and electric vehicle.    ADVANTAGE - The non-aqueous-electrolyte lithium ion secondary cell has excellent durability and output characteristics.    DETAILED DESCRIPTION - A non-aqueous-electrolyte lithium ion secondary cell has a positive electrode with a positive electrode compound material containing a positive electrode active material, an electroconductive material, a binder and an activated carbon, a negative electrode having a negative electrode compound material containing a carbon material and a binder, and a non-aqueous electrolyte formed by dissolving an electrolyte in a nonaqueous solvent. The electrolyte contains a lithium salt containing fluorine element and a subsidiary component electrolyte of formula (I).    M=transition metal or element of group (III, IV or V) in periodic table;    A(power)(a+)=metal ion, proton or onium ion;    a,b=1-3;    p=b/a;    m=1-4;    n=0-8;    q=0 or 1;    R1=(1-10C alkylene, halogenated 1-10C alkylene, 6-20C arylene or halogenated 6-20C arylene) optionally having substituent and hetero atom;    R2=halogen, (1-10C alkyl, 1-10C alkyl halide, 6-20C aryl, halogenated 6-20C aryl) optionally having substituent and hetero atom or X3R3;    X1-X3=oxygen, sulfur or NR4;and    R3,R4=H, (1-10C alkyl, 1-10C alkyl halide, 6-20C aryl or halogenated 6-20C aryl) optionally having substituent and hetero atom.    R2 combine to form a ring. R3 and R4 combine to form a ring.    DESCRIPTION OF DRAWING(S) - The drawing shows the sectional view of the non-aqueous-electrolyte lithium ion secondary cell. (Drawing includes non-English language text)    Non-aqueous-electrolyte lithium ion secondary cell (1)    Positive electrode (2)    Negative electrode (3)    Separator (4)    Positive electrode current collection lead (28)