A back light boost converter includes an analog circuit, an enable controller, a logic device, and a digital PWM controller. The analog circuit generates a switch signal and a feedback signal based on a first pulse signal. The enable controller generates an enable signal based on an LED on ratio signal, an LED on cycle signal, a duty cycle signal, and a frequency signal. The logic device generates a second pulse signal based on the feedback signal and the enable signal. The digital PWM controller outputs the first pulse signal with increasing duty cycles in a plurality stages.