A control circuit applied in a light emitting diode (LED) driver includes a counter, a sample circuit, and a signal source. The counter counts a parameter indicating the duty cycle width of a dimming signal in response to a front edge of the dimming signal. The sample circuit obtains a sample signal by means of sampling the most significant bit (MSB) of the parameter in response to the rear edge of the dimming signal. The duty cycle width is determined to be greater than a threshold value and smaller than that when the sample signal corresponds with a terminal value and an initial value, respectively. The signal source provides a reference voltage corresponding to first level and that corresponding to second level, higher than the first level, to drive a boost converter of the LED driver in response to the terminal value and the initial value, respectively.