An LED driving device and a constant power dimming circuit and dimming method therefor. The constant power dimming circuit comprises a line voltage compensation module, a modulation module, a filtering module, and a constant current source module. The line voltage compensation module detects changes in line voltage and outputs a first reference voltage. The modulation module modulates the first reference voltage and outputs to the filtering module a second reference voltage. The filtering module filters the second reference voltage signal and then outputs a third reference voltage to the constant current source module. The constant current source module outputs constant current to drive an LED load to operate. By controlling a constant current source circuit, when the duty cycle of the PWM signal is not changed but a mains input voltage is changed, the input power of the system can be maintained constant, and voltage flicker is reduced.