In another preferable aspect, a composite oxide contained in the active material for a battery according to the first embodiment contains two or more elements which have different valences from each other at sites corresponding to the Ti sites in the composite oxide Li2+wNa2Ti6O14+δ. Such a composite oxide has a larger potential gradient during the charge-and-discharge, and therefore is preferable. The reason why the potential gradient is larger is, for example, that there are two or more elements having electrical correlations with the oxide ion different from each other at sites corresponding to titanium sites in the crystal structure of the composite oxide Li2+wNa2Ti6O14+δ, and thus multiple sites, which have a difference from each other in electrical correlation with the Li ion and with the oxide ion respectively, are generated at these sites. More specifically, an element having a higher valence contained in these sites has a tendency to take more of an electron cloud of the oxide ion and, on the other hand, an element having a lower valence has a tendency in which the correlation between the oxide ion and the electron cloud is weak. Therefore, a difference occurs in an electrical state of the oxide ion near to the lithium host site, and as a result, the electrical correlation which is provided to the lithium ion from the lithium host site becomes different. Consequently, the variation in the potential due to the insertion and extraction of the lithium ion increases.