A switching converter has an input port for receiving an input voltage and an output port for providing an output voltage. The switching converter has a power stage, an energy stored circuit, a power conversion circuit and a control circuit. The power stage has an input terminal coupled to the input port and an output terminal coupled to the output port. The energy stored circuit is charged by the input voltage and provides a first bias voltage which maintains a predetermined time period after the input voltage is less than a predetermined voltage level. The power conversion circuit provides a second bias voltage. The control circuit provides a control signal to control the power stage and discharges the output voltage based on a discharge control signal, wherein the control circuit is powered by either the first bias voltage or the second bias voltage.