The purpose of this study is to investigate the cooling performance of radial heat sink used for high power LED lightings by natural convection cooling with surrounding air. Experimental and numerical analyses are carried out together. Parametric studies are performed to compare the effects of geometric parameters in radial heat sink such as the number of fins, fin height, fin length, and thickness of fin base as well as the surface coatings of radial heat sink. In this study, the cooling of 60 W LED lamp is examined with radiative heat transfer considered as well as natural convection. Numerical results show the optimum condition when the number of fin is 40, heat sink height is 120 mm, fin length is 15 mm, and fin base thickness is 3 mm. The difference in temperature of the LED metal PCB is within $1^{circ}C$ between numerical analyses and experimental results. Also, the CNT coating on the heat sink surface is found to increase the cooling performance significantly.