A control circuit for controlling a power converter can include: a constant voltage output module, a constant current output module, and a power stage circuit; and where the control circuit is configured to select one of a first feedback signal representative of output information of the constant current output module, and a second feedback signal representative of output information of the constant voltage output module as a feedback input signal based on operation states of the constant current output module and the constant voltage output module, in order to control a switching state of a power switch of the power stage circuit.