A charging discharging apparatus is applied to two super capacitor modules. The charging discharging apparatus includes a control unit, a first switch unit, a second switch unit, a third switch unit, a fourth switch unit, a first charging switch unit, a second charging switch unit and a charging unit. When an input power apparatus sends an input power to the charging discharging apparatus, the charging discharging apparatus enters a charging mode, so that the super capacitor module having the lower voltage is charged until the voltages of the two super capacitor modules are equal, and then the two super capacitor modules are charged simultaneously in parallel. When the input power apparatus stops sending the input power to the charging discharging apparatus, the two super capacitor modules discharge in series.