In this work, significance of heat sink fins numbers on the heat dissipation of single chip high power LED package was addressed. The investigation was carried out through simulation by utilizing Ansys version 11. In this work, the heat sink fin numbers were increased from 4 fins to 6 fins, 8 fins, 10 fins and 12 fins respectively. The heat dissipation were evaluated in terms of operating junction temperature, thermal resistance and von Mises stress of the LED chip. Results of the analysis showed that with the increment of heat sink fins, the surface area of the heat sink also increases which in turn reduces the junction temperature of the GaN chip.