A secondary-side bucking and current-stabilizing flyback power converter adopts a dual-stage isolated circuit architecture and outputs a constant output current to drive a low-power LED module, and its primary stage adopts a flyback circuit architecture with a primary regulated voltage, and its secondary stage adopts of a buck circuit architecture of the current stabilizer, so that after the primary stage converts the constant voltage, the current stabilizer senses the load effect of the output current at the LED module to regulate the output cycle and maintain the total output of the output current constant and reduce the ripple amplitude, so as to achieve a non-strobe output result and improve the illumination effect of the LED module.