A control circuit is developed to adaptively operate a power converter at quasi-resonance (QR) and in a continuous current mode (CCM) to achieve high efficiency. The control circuit includes a PWM circuit generating a switching signal coupled to switch a transformer. A signal generation circuit generates a ramp signal and a pulse signal. The pulse signal is generated in response to the ramp signal for switching on the switching signal. A feedback circuit produces a feedback signal according to an output load of the power converter. The feedback signal is coupled to switch off the switching signal. A detection circuit is coupled to the transformer for generating a valley signal in response to the waveform of the transformer. The valley signal is further coupled to generate the pulse signal when the ramp signal is lower than a threshold. The level of the threshold is correlated to the feedback signal.