A voltage-waveform detector produces a voltage-feedback signal and a discharge-time signal by multi-sampling a voltage signal of a transformer. The discharge-time signal represents a discharge time of a secondary-side switching current. A voltage-loop error amplifier amplifies the voltage-feedback signal and generates a control signal. An off-time modulator correspondingly generates a discharge-current signal and a standby signal in response to the control signal and an under-voltage signal. The under-voltage signal indicates a low supply voltage of the controller. An oscillator produces a pulse signal in response to the discharge-current signal. The pulse signal determines the off-time of the switching signal. A PWM circuit generates the switching signal in response to the pulse signal and the standby signal. The standby signal further controls the off-time of the switching signal and maintains a minimum switching frequency. The switching signal is used for regulating the output of the power supply.