Junction temperature is an important parameter in thermal management of LEDs (Light emitting diodes) system. The junction temperature of three different types of LED is calculated numerically. Three dimension numerical simulation using ANSYS-Icepak 15 software package is presented for all cases. Appropriate heat sink is designed for each type of LED and investigates the effect of the fins height on the junction temperature. The increasing in electrical current utilized to driving the LEDs has concentrate high notice on the thermal management in the evolution of LED system. A felicitous design should have minimum thermal resistance between the heat sink base and the junction that depends on conduction heat transfer. The results showed the increase in a heat sink height 10% dissipate more heat transfer from the LEDs system at approximately 15%.