As an alternative technique to lead-acid batteries, the present invention provides an inexpensive 2 V non-aqueous electrolyte secondary battery having excellent cycle life at a high rate by preventing volume change during charge and discharge. The non-aqueous electrolyte secondary battery uses: a positive electrode active material having a layered structure, being represented by chemical formula Li.sub.1.+-..alpha.[Me]O.sub.2, where 0.ltoreq..alpha.<0.2, and Me is a transition metal including Ni and at least one selected from the group consisting of Mn, Fe, Co, Ti and Cu, and including elemental nickel and elemental cobalt in substantially the same ratio; and a negative electrode active material including Li.sub.4Ti.sub.5O.sub.12(Li[Li.sub.1/3Ti.sub.5/3]O.sub.4).