A resonant half-bridge flyback power converter includes: a first transistor and a second transistor which form a half-bridge circuit; a transformer and a resonant capacitor connected in series and coupled to the half-bridge circuit; and a switching control circuit configured to generate a first driving signal and a second driving signal to control the first transistor and the second transistor respectively for switching the transformer to generate an output voltage. The first driving signal is configured to magnetize the transformer. The second driving signal includes at most one pulse between two consecutive pulses of the first driving signal. The switching control circuit generates a skipping cycle period when an output power is lower than a predetermined threshold. A resonant pulse of the second driving signal is skipped during the skipping cycle period. The skipping cycle period is increased in response to the decrease of the output power.