A capacitor discharging circuit and a power converter having the capacitor discharging circuit are disclosed. The capacitor discharging circuit comprises a conversion module connected with the two terminals of the capacitor, an AC power-off detecting unit used to detect on-off state of AC power, and a control unit. The conversion module comprises an energy consumption unit. When AC power is disconnected, the AC power-off signal generated by the AC power-off detecting unit intervenes the control unit to control the energy consumption unit to consume the energy stored in the capacitor.