The charge neutrality in the crystal structure of the composite oxide can be maintained by satisfying the conditions of the formula (2). The composite oxide Li2+wNa2?xM1yTi6?zM2zO14+δ whose charge neutrality is maintained is a substituted oxide in which a part of the Ti sites is properly substituted by the cation M2 in the crystal structure of the composite oxide represented by the general formula of Li2+wNa2Ti6O14+δ. In addition, the composite oxide Li2+wNa2?xM1yTi6?zM2zO14+δ in which charge neutrality is maintained and y is greater than 0 is a substituted oxide in which a part of the Na sites is properly substituted by the cation M1 in the crystal structure of the composite oxide represented by the general formula of Li2+wNa2Ti6O14+δ. In addition, in the composite oxide Li2+wNa2?xM1yTi6?zM2zO14+δ whose charge neutrality is maintained, a part corresponding to a part of the Na sites in the crystal structure of the composite oxide represented by the general formula of Li2+wNa2Ti6O14+δ can stably exist as a vacancy in the crystal structure. By containing the substituted oxide in which the cation M2 is properly substituted in the crystal structure of the composite oxide represented by the general formula of Li2+wNa2Ti6O14+δ and which contains the properly substituted cation M1 and/or the vacancy which can stably exist in the crystal structure of the composite oxide represented by the general formula of Li2+wNa2Ti6O14+δ, as described above, the active material for a battery according to the first embodiment can make a coordination environment of the oxide ions to void sites where the lithium ions are inserted uniform. This is a reason why the composite oxide, which can be contained in the active material for a battery according to the first embodiment, can show a continuous potential change within a potential range of 1.0 V to 1.45 V (vs. Li/Li+). On the other hand, a composite oxide in which the uniformity of the coordination environment of the oxide ions to the void sites is low exhibits a potential step in the charge-and-discharge curve, i.e., a steep change in the potential.