A control circuit for a flyback converter is configured to adjust a conduction time of an auxiliary switch of the flyback converter in accordance with a drain-source voltage of a main switch of the flyback converter when the main switch is turned on, in order to achieve zero-voltage switching of the main switch. The flyback converter can include: a main power stage having the main switch to control energy storage and transmission of a transformer; and a clamp circuit having an auxiliary switch to provide a release path for releasing energy of leakage inductance of the transformer.