A control circuit for use in a power converter has a multi-function terminal, a current comparator circuit, and an under-voltage detection circuit. The current comparator circuit compares current flowing through a power switch of the power converter with a reference value through the multi-function terminal when the power switch is on, and turns the power switch off when the current reaches the reference value. The under-voltage detection circuit determines whether an input voltage of the power converter is less than a predetermined value through the multi-function terminal when the power switch is turned off.