A Light-Emitting Diode (LED) driver circuit is disclosed that controls the brightness of light generated by a LED that is coupled between a first terminal and a second terminal in response to a user supplied brightness control signal. A constant current source generates a constant current that is supplied to the LED and to a shunt circuit, which his connected in parallel with the LED. A brightness control circuit generates a pulse signal having a duty cycle that is proportional to the brightness control signal, and controls the shunt circuit such that, when said pulse signal is high, the constant current is passed through the shunt circuit and the LED is turned off, and when the pulse signal is low, the constant current is passed through the LED. The duty cycle of the brightness control signal is adjusted to adjust the LED's brightness, while the LED color remains constant.