A power supply and a method of power supplying for converting an external alternating power into an output power with appropriate voltage and power are disclosed. The power supply includes an input charging unit, an input filtering unit, a regulating unit, a transformer, a controller, an output unit, an output capacitor, a switching unit and a feedback unit. The regulating unit is connected to the input filtering unit and comprises a regulating capacitor and a regulator connected in series. The regulator is controlled by the controller to perform one of the working modes including initial open circuit, power on conduction, short circuit normal operation and over-voltage open circuit protection. Therefore, the present invention overcomes the problem of inrush current upon powering on, and particularly, the controller performs digital operation with flexibility to meet actual requirements by updating appropriate firmware of software program.