A flyback power converter circuit converting an input voltage to an output voltage includes a transformer, a power switch, a synchronous rectifier (SR) switch, and a secondary side control circuit. The secondary side control circuit controls the SR switch to be ON when the power switch is OFF. The secondary side control circuit includes a driving switch for controlling the SR switch, a synchronous control circuit powered by a voltage related to the output voltage, which controls the driving switch to operate the SR switch, and a clamping circuit including a clamping switch and a clamping switch control circuit. The clamping switch control circuit controls the clamping switch according to a current inflow terminal voltage of the clamping switch and/or the voltage related to the output voltage, such that, during a secondary side power-on period, an equivalent impedance of the current inflow terminal of the clamping switch is smaller than a predetermined clamping impedance.