The invention relates to a non-aqueous electrolyte battery, a battery pack and a vehicle. According to one embodiment, a non-aqueous electrolyte battery includes an outer case (2), a positive electrode (5) housed in the outer case and containing a positive electrode active material, a negative electrode (3) housed in the outer case (2) and containing a monoclinic crystal [beta]-type titanium composite oxide, and a non-aqueous electrolyte filled in the outer case (2). An absolute value of a gradient of a potential of the negative electrode (3) is larger than that of the positive electrode (5). Wherein, each of the gradients of a potential of the negative and positive electrodes (3,5) is found from variations in potential which come at the state of full charge on an open-circuit potential curve drawn from potentials of the positive electrode (5) and the negative electrode (3).