An LED light source device using light from luminescent elements at a high level of uniformity and efficiency, and to conduct irradiation with a high level of design freedom an LED light source device is equipped with luminescent elements and a translucent light-guiding member. The translucent light-guiding member has a central convex lens with a first cylindrical light-guiding part formed on the outer periphery of the central convex lens and a second cylindrical light-guiding part formed on the outer periphery of the first cylindrical light-guiding part, such that an air layer is formed between the outer peripheral surface of the first cylindrical light-guiding part and the inner peripheral surface of the second cylindrical light-guiding part, the outer peripheral surface of the first cylindrical light-guiding part and the outer peripheral surface of the second cylindrical light-guiding part being rotated quadratic surfaces with the same focal point.