Provided are a radiator which can spread a heat-exchanging medium such as air without enlarging the outside dimension, thereby to improve the radiation, and a lighting device having that radiator. The radiator (1) is constituted to comprise an inner cylinder (12), to which the heat from LED modules (2, 2 - - -) is transferred, first fins (13, 13, - - -) protruded in an intersecting direction from the outer face (12a) of the inner cylinder (12), and an outer cylinder (14) disposed to enclose the inner cylinder (12). Without enlarging the outside size of the radiator (1), the radiation area can be increased to improve the radiation. Moreover, the heat can be efficiently transferred from the surfaces of the inner cylinder (12), the outer cylinder (14) and the first fins (13, 13, - - -), which form a draft passage (or a medium passage) altogether, to the air having a flow velocity increased by the chimney effect, and the air can be distributed between and to the roots of the adjoining first fins (13, 13, - - -). Thus, the radiator (1) can improve its radiation without having its outside size increased.