A compressor driving apparatus and an air conditioner including the same, whereby the compressor driving apparatus includes a capacitor connected to a DC terminal, an inverter, including a plurality of three-phase switching devices, to convert DC power from the capacitor into AC power to drive a compressor motor, an output current detector to detect output current flowing in the motor, and a controller to output a switching control signal for controlling the inverter based on the output current, wherein the controller performs control such that some of the three-phase switching devices in the inverter are turned on or off in a compressor preheating mode.