An LED constant-voltage dimming power supply being electrically connected to a dimmer and configured for changing duty ratio of output voltage thereof according to a controlling signal from the dimmer, includes a constant-voltage source, a damping discharge circuit module, a phase detecting circuit module, a duty ratio controlling module, and a switcher. The damping discharge circuit module is electrically connected to an input end of the constant-voltage source. The phase detecting circuit module is electrically connected to an output end of the constant-voltage source. The duty ratio controlling module is coupled to the phase detecting circuit. The switcher is electrically connected to the duty ratio controlling module. The LED constant-voltage dimming power supply adjusts the luminance of the LED lamp and has high universality. Moreover, each of lots of LED lamps has high consistency during adjusting its luminance.