In comparison with some other light sources, LED has merits such as increased life expectancy, fast response, pollution free, and high energy efficiency. Lately, due to development of LED with high brightness and capacity, LED has widely used in many industrial fields such as automotive, aviation, display, transportation and special lighting applications. Since the high heat generation of LED chips can cause a reduction in lifetime, degradation of luminous efficiency, and variation of color temperature, studies have been carried out on the optimization of LED packaging and heat sinks. In this study, experiments on measuring the heat generation rate of LED and the cooling performance of a heat sink were carried for analyzing the thermal characteristics of LED lighting system in free convection. From the results, dimensionless correlation on the cooling performance of heat sink in natural convection was proposed with Nusselt number and Rayleigh number as a guideline for designing cooling device of LED lightings.