An LED driver includes at least two interlocked closed feedback loops. One feedback loop controls the duty cycle of the on/off times of a switch connected in series to the LED string, and the other feedback loop controls the duty cycle of the on/off times of a power switch in the switching power converter that provides a DC voltage applied to the LED string. The LED driver of the present invention achieves fast control of the LED brightness and current sharing among multiple LED strings simultaneously in a power-efficient and cost-efficient manner.