A flyback power converter includes: a power transformer, a primary side control circuit, a secondary side control circuit, and an active clamp snubber including a snubber switch and a control signal generation circuit. The control signal generation circuit controls the snubber switch to be conductive during a soft switching period in an OFF period of a primary side switch within a switching period of the switching signal, whereby the primary side switch achieves soft switching. A starting time point of the soft switching period is determined by a current threshold, so that a secondary side current is not lower than the current threshold at the starting time point, whereby the secondary side control circuit keeps the SR switch conductive at the starting time point. The secondary side control circuit turns OFF the SR switch when the secondary side current is lower than the current threshold.