An apparatus and a method for power supply are provided. In the invention, the residual standby power can be quickly discharged by an additional fast discharging unit within a predetermined time when an external AC power (for example, city power) received by the power supply apparatus capable of supporting ATX (Advanced Technology eXtended) specification is unavailable (for example, power trip). Accordingly, any host system applied with the inventive power supply apparatus and method would not be inoperable when the received external AC power (city power) is recovered, and thus effectively promoting the stability of the applied host system.