A capacitor discharging circuit and a converter are disclosed. The converter comprises: a capacitor connected between the live line and null line of an AC power input terminals, a conversion module coupled to the capacitor and comprising an energy storage component at least, an energy transfer unit coupled with the energy storage component and the capacitor, an AC power-off detecting unit and a control unit; wherein the energy transfer unit comprises a switch device; when AC power is disconnected, the AC power-off signal triggers the control unit to output a switch driving signal, controlling the operation of the energy transfer unit to transfer the energy stored in the capacitor to the energy storage component to discharge the capacitor.