A battery pack comprising: a non-aqueous electrolyte secondary battery including: (a) a battery element (59, 35) including a positive electrode, a negative electrode, and a separator which are spirally wound or stacked, the separator is disposed between the positive electrode and the negative electrode, the battery element (59, 35) including a non-aqueous electrolyte composition; (b) a flexible covering member (57, 31), formed of a first laminated film, which covers the battery element, the first laminated film is composed of a first heat-bonding layer, a first metal layer, and a first outer covering layer which are laminated successively, wherein the flexible covering member is sealed along around the battery element (59, 35) while leaving electrode terminals (55a, 55b) of the positive and negative electrodes (51, 52) extended to outside the battery element (59, 35); (c) a rigid covering member (32, 41) which covers the non-aqueous electrolyte secondary battery together with the flexible covering member, the rigid covering member is formed of a second laminated film composed of a second heat-bonding layer, a second metal layer, and a second outer covering layer which are laminated successively; and (d) a protection circuit board, housed in the rigid covering member, for controlling a voltage and a current of the non-aqueous electrolyte secondary battery, wherein the battery element (59, 35) and the flexible covering member are adhered to each other, and wherein the flexible covering member and the rigid covering member are bonded by melting the second heat-bonding layer without melting the first outer covering layer, wherein the first outer covering layer has a melting temperature higher than that of the second heat-bonding layer. a non-aqueous electrolyte secondary battery including: (a) a battery element (59, 35) including a positive electrode, a negative electrode, and a separator which are spirally wound or stacked, the separator is disposed between the positive electrode and the negative electrode, the battery element (59, 35) including a non-aqueous electrolyte composition; (b) a flexible covering member (57, 31), formed of a first laminated film, which covers the battery element, the first laminated film is composed of a first heat-bonding layer, a first metal layer, and a first outer covering layer which are laminated successively, wherein the flexible covering member is sealed along around the battery element (59, 35) while leaving electrode terminals (55a, 55b) of the positive and negative electrodes (51, 52) extended to outside the battery element (59, 35); (c) a rigid covering member (32, 41) which covers the non-aqueous electrolyte secondary battery together with the flexible covering member, the rigid covering member is formed of a second laminated film composed of a second heat-bonding layer, a second metal layer, and a second outer covering layer which are laminated successively; and (d) a protection circuit board, housed in the rigid covering member, for controlling a voltage and a current of the non-aqueous electrolyte secondary battery, wherein the battery element (59, 35) and the flexible covering member are adhered to each other, and wherein the flexible covering member and the rigid covering member are bonded by melting the second heat-bonding layer without melting the first outer covering layer, wherein the first outer covering layer has a melting temperature higher than that of the second heat-bonding layer. (a) a battery element (59, 35) including a positive electrode, a negative electrode, and a separator which are spirally wound or stacked, the separator is disposed between the positive electrode and the negative electrode, the battery element (59, 35) including a non-aqueous electrolyte composition; (b) a flexible covering member (57, 31), formed of a first laminated film, which covers the battery element, the first laminated film is composed of a first heat-bonding layer, a first metal layer, and a first outer covering layer which are laminated successively, wherein the flexible covering member is sealed along around the battery element (59, 35) while leaving electrode terminals (55a, 55b) of the positive and negative electrodes (51, 52) extended to outside the battery element (59, 35); (c) a rigid covering member (32, 41) which covers the non-aqueous electrolyte secondary battery together with the flexible covering member, the rigid covering member is formed of a second laminated film composed of a second heat-bonding layer, a second metal layer, and a second outer covering layer which are laminated successively; and (d) a protection circuit board, housed in the rigid covering member, for controlling a voltage and a current of the non-aqueous electrolyte secondary battery, wherein the battery element (59, 35) and the flexible covering member are adhered to each other, and wherein the flexible covering member and the rigid covering member are bonded by melting the second heat-bonding layer without melting the first outer covering layer, wherein the first outer covering layer has a melting temperature higher than that of the second heat-bonding layer.