A flyback power converter circuit includes: a transformer; a primary side switch, for controlling a primary winding to convert an input voltage to an output voltage and an internal voltage; a primary side control circuit, which is powered by the internal voltage; the primary side control circuit generates a switching signal according to a feedback signal, to operate the primary side switch; a secondary side control circuit, which generates the feedback signal according the output voltage; and a dummy load circuit, which is coupled to the output voltage, wherein when the output voltage drops to or is lower than a predetermined threshold, the dummy load circuit generates a dummy load current, to determine the feedback signal, so that the internal voltage is not undesirably low. When the output voltage exceeds the predetermined threshold, the dummy load circuit adjusts the dummy load current to zero current.