Individual LED dimming control is required for RGB light mixing applications by controlling LED currents independently with multiple-output LED drivers. In this thesis, a single-inductor multiple-output dimmable LED driver with buck converter is designed. According to the overall output power and input voltage conditions, the buck converter with the primary-side control can be operated in QR mode, frequency limitation and frequency reduction mode. The varied frequency controlled signal method is proposed to control the dimming sequence and the conducting times of the RGB LED strings. Finally, the buck-type SIMO LED driver with the universal input voltages 90 - 264 Vrms to drive Red (25 V/0.2 A), Green (40 V/0.2 A) and Blue (40.5 V/0.2 A) LED lamps is implemented. The dimming range is from 5 % to 100 % individually. The highest error of the dimming is 10% and the highest efficiency is 94%.