A constant power control circuit driving an external device receiving an input voltage and generating an output voltage is provided. A first conversion circuit converts the voltage difference between the input voltage and the output voltage to generate a charge current. An energy storage circuit is charged during a charging period by the charge current to provide a stored voltage. The charging period is terminated in response to the stored voltage reaching a predetermined voltage. A control circuit adjusts a control signal according to a length of the charging period. A second conversion circuit generates a counting voltage according to the control signal. The counting voltage is inversely proportional to the voltage difference. A third conversion circuit converts the counting voltage into a limitation current. A driving circuit compares the setting current and the limitation current to generate a driving signal and send it to the external device.