LEDs have small size, long lifespan, high reliability, low power consumption and high color efficiency. Using such a characteristics, LED Back Light Unit has been studying actively. This paper proposes LED driver to minimize power consumption due to LED forward voltage($V_F$) difference and temperature rising. Compared to conventional LED driver, the proposed driver have excellent stability, brief structure and linear output voltage of DC-DC boost converter. Proposed LED Driver circuit was designed using 0.35um CMOS technology. And its operation was verified through simulation.