A flyback power converter circuit includes: a power transformer, a primary side switch and a conversion control circuit. In a DCM, during a dead time, the conversion control circuit calculates an upper limit frequency corresponding to output current according to a frequency upper limit function, and obtains a frequency upper limit masking period according to a reciprocal of the upper limit frequency, wherein the frequency upper limit masking period is a period starting from when the primary side switch is turned ON. During an upper limit selection period, the conversion control circuit selects a valley among one or more valleys in a ringing signal related to a voltage across the primary side switch as an upper limit locked valley, so that the conversion control circuit once again turns ON the primary side switch at a beginning time point of the upper limit locked valley.