A low power bandgap voltage reference circuit for Low Dropout Regulator(LDO) is proposed. The power consumption is effectively decreased by setting the differential input pair of the amplifier into sub-threshold region and by using a zero power start-up circuit. The bandgap voltage reference circuit is implemented by MIXIC’s 0.35 μm CMOS process. The results indicate that the temperature coefficient of the output voltage is 33 ppm/℃, and the total current consumption is 12 μA only.