A flyback-based power conversion apparatus and a power conversion method thereof are provided. By switching first and second detection switches disposed in a control chip and coupled to a multi-function pin of the control chip at different timings, the present invention applies a collocation of a voltage-current detection auxiliary circuit and a current detection circuit at a certain timing to execute a detection of the AC input voltage received by a flyback power conversion circuit, and the present invention applies a collocation of the auxiliary voltage-current detection circuit, an over temperature protection unit and an over voltage protection unit at another timing to execute detections of an over temperature protection and an over voltage protection. As the result, a single multi-function detection pin of the control pin is corresponding to a plurality of related function detections, so as to reduce the production cost of manufacturing the control chip.