A heat dissipation structure including a plurality of heat dissipating members, and a support plate for supporting the heat dissipating members. Each of the heat dissipating members includes a plurality of cushion members each having a hollow or a solid shape, and a heat conduction sheet covering an outer surface of the cushion members. The support plate includes a plurality of grooves for supporting the heat dissipating members in a direction orthogonal to a longitudinal direction of the heat dissipating members. Each of the grooves is a curved recess portion formed in a thickness direction, opened to the side of the heat dissipating member, formed to have a radius of curvature larger than a radius of curvature of the heat dissipating member, and to have a depth smaller than a circular conversion diameter of the heat dissipating member, and a battery provided with the heat dissipating structure.