A negative electrode active material according to an embodiment includes at least a titanic oxide compound. The intensity ratio of an infrared absorption spectrum after pyridine adsorption and desorption on a surface of the negative electrode active material satisfies relationships represented by the following formula [{I(3663 cm−1)/I(3738 cm−1)}>0.7] and the following formula [{I(2981 cm−1)/I(2930 cm−1)}