NOVELTY - Lithium secondary battery (I) comprises: a positive electrode (2) including lithium-nickel-based oxide or a lithium-nickel-manganese-based oxide; a negative electrode (4) including a lithium metal, a lithium-containing alloy, a material which is capable of reversible intercalation/deintercalation of lithium ions or a material which is capable of reversibly forming a lithium-containing compound; and a non-aqueous electrolyte (26).    USE - (I) is useful as power source for many types of electrical equipment, e.g. portable telephones, cellular phones, game machines, portable televisions, notebook computers and calculators.    ADVANTAGE - The non-aqueous electrolyte prevents (I) from swelling, while maintaining the electrochemical properties of (I). (I) has good swelling inhibition properties and good cycle-life characteristics at high temperature. The electrolyte can solve the problem of deterioration of battery performance such as capacity and cycle life even when a lithium-nickel-based or lithium-nickel-manganese-based oxide is used as positive active material. The electrolyte shows good discharge characteristics even when graphite, especially natural graphite, is used as a negative material.    DETAILED DESCRIPTION - Lithium secondary battery (I) comprises: a positive electrode (2) including lithium-nickel-based oxide or a lithium-nickel-manganese-based oxide; a negative electrode (4) including a lithium metal, a lithium-containing alloy, a material which is capable of reversible intercalation/deintercalation of lithium ions or a material which is capable of reversibly forming a lithium-containing compound; and a non-aqueous electrolyte (26), where the non-aqueous electrolyte comprises a lithium salt, an organic solvent comprising a mixed solvent of a carbonate solvent and an aromatic hydrocarbon solvent, a first additive compound (0.01-5 wt.%) comprising pyrrolidin-2-one compound of formula (A) or their derivatives, and a second additive compound (0.01-5 wt.%) comprising (1,3)dioxolan-2-one compound of formula (B).    R1 = alkyl, ester radical or aliphatic carbonate radical; and    X = halogen radical, cyano radical or nitro radical.    DESCRIPTION OF DRAWING(S) - The figure shows a prismatic lithium secondary battery.    Positive electrode (2)    Negative electrode (4)    Electrode assembly (8)    Battery case (10)    Electrolyte. (26)