A constant current control circuit includes a sample and hold unit coupled to a current sensing resistor of a power converter, for storing a current sensing voltage of the current sensing resistor; a first capacitor for storing a comparison voltage; a discharge unit coupled between the sample and hold unit and the first capacitor, for controlling a discharge current of the first capacitor according to a reference voltage and the current sensing voltage stored in the sample and hold unit; a charge unit coupled to the first capacitor, for controlling a charging current of the first capacitor according to the reference voltage and a ground voltage; and a comparator for comparing the comparison voltage with the reference voltage to generate a comparison result, and outputting a control signal according to the comparison result, in order to control a duty cycle of the power converter.