An LED driver is disclosed that drives LEDs connected in parallel. Instead of applying current to all the parallel-connected LEDs at the same time, under control of a common PWM brightness control signal, the application of current to each parallel path is staggered by using staggered brightness control signals. The turning on of the LEDs in the different parallel paths will have the same duty cycle but will be out of phase. This reduces ripple in the power supply by reducing the magnitude of the instantaneous current sink. In one embodiment, a shift register contains a binary representation of the PWM duty cycle, and a clock shifts the bits along the shift register. The PWM brightness control signals for each parallel path of LEDs are tapped from different positions along the shift register so that the PWM brightness control signals are identical but staggered.