According to one embodiment, there is provided a battery including a positive electrode, and a negative electrode. The positive electrode contains a lithium-cobalt composite oxide and a lithium-manganese composite oxide. The negative electrode contains a lithium titanium composite oxide. The battery satisfies the following formula (1). In addition, an open circuit voltage (OCV) of the positive electrode when the battery is discharged to 1.8 V at 0.2 C is 3.6 V (Li v.s. Li+) or more. (Qp/Qn)>1.1  (1) Qp is a charge capacity (mAh/m2) of the positive electrode per unit area, and Qn is a charge capacity (mAh/m2) of the negative electrode per unit area.