An LED driver is disclosed that boosts an input voltage to drive any number of LEDs in series. The driver includes a switch-mode current regulator that supplies regulated current pulses to the LEDs. No high voltage output capacitor is used to smooth the current pulses, so the LEDs are turned on any off at the switching frequency. Also, no blocking diode between the switching transistor and the LEDs is used. The cathode of the “bottom” LED in the string is connected to ground via a current sense resistor. In parallel with the sense resistor is connected an RC filter using a small, low voltage filter capacitor. The RC filter provides a substantially smooth feedback voltage for the current regulator to control the duty cycle of the switching transistor so that the feedback voltage matches a reference voltage.