The subscript x in the general formula of Li2+wNa2?xM1yTi6?zM2zO14+δ for the composite oxide indicates an Na amount in the crystal structure in this composite oxide. The active material for a battery according to the first embodiment can control an average operating potential of an electrode containing the active material for a battery within a range of 1.2 V (vs. Li/Li+) to 1.5 V (vs. Li/Li+) to the oxidation-reduction potential of the metal lithium by changing the Na amount in the crystal structure, i.e., the value of the subscript x, whereby the operating potential of the battery can be easily designed. From a different aspect, the subscript x is an index showing a ratio of a part which is substituted by the cation M1 or the vacancy in the substituted composite oxide, among the sites corresponding to the Na sites in the composite oxide Li2+wNa2Ti6O14+δ. The subscript x is within a range of 0<x<2, preferably 0.1≤x≤0.9, more preferably 0.25≤x≤0.75.