A compressor driving apparatus comprising: a compressor including a compressor motor and a magnetic bearing; a coil driver including a switching element and to apply a current to a bearing coil of the magnetic bearing by a switching operation of the switching element to cause a rotor of the compressor motor to be levitated from or land on the magnetic bearing; and a controller to control the switching element of the coil driver, wherein, when the rotor of the compressor motor lands, the controller is configured to gradually decrease the current flowing through the bearing coil, characterized in that when the rotor of the compressor motor lands, the controller is configured to alternate first and second modes with each other, the first mode being a mode in which the current stored in the bearing coil is discharged, and the second mode being a mode in which current flows through the bearing coil by power stored in a capacitor, wherein the coil driver (437, 1200) comprises: a capacitor (Cbs) to store direct current power; a first switching element connected between one end of the capacitor (Cbs) and one end of the bearing coil; a first diode element connected between the other end of the capacitor (Cbs) and the one end of the bearing coil; a second diode element connected between the one end of the capacitor (Cbs) and the other end of the bearing coil; a second switching element connected between the other end of the capacitor (Cbs) and the other end of the bearing coil; and the bearing coil is connected between the first switching element and the first diode element and between the second diode element and the second switching element, wherein when the first switching element and the second switching element are turned on simultaneously during the second mode, a first current flows sequentially along the capacitor (Cbs), the first switching element, the bearing coil, and the second switching element, and wherein when the first switching element is turned off and the second switching element is turned on during the first mode, a second current flows along the first diode element, the bearing coil, and the second switching element. a compressor including a compressor motor and a magnetic bearing; a coil driver including a switching element and to apply a current to a bearing coil of the magnetic bearing by a switching operation of the switching element to cause a rotor of the compressor motor to be levitated from or land on the magnetic bearing; and a controller to control the switching element of the coil driver, wherein, when the rotor of the compressor motor lands, the controller is configured to gradually decrease the current flowing through the bearing coil, characterized in that when the rotor of the compressor motor lands, the controller is configured to alternate first and second modes with each other, the first mode being a mode in which the current stored in the bearing coil is discharged, and the second mode being a mode in which current flows through the bearing coil by power stored in a capacitor, wherein the coil driver (437, 1200) comprises: a capacitor (Cbs) to store direct current power; a first switching element connected between one end of the capacitor (Cbs) and one end of the bearing coil; a first diode element connected between the other end of the capacitor (Cbs) and the one end of the bearing coil; a second diode element connected between the one end of the capacitor (Cbs) and the other end of the bearing coil; a second switching element connected between the other end of the capacitor (Cbs) and the other end of the bearing coil; and the bearing coil is connected between the first switching element and the first diode element and between the second diode element and the second switching element, wherein when the first switching element and the second switching element are turned on simultaneously during the second mode, a first current flows sequentially along the capacitor (Cbs), the first switching element, the bearing coil, and the second switching element, and wherein when the first switching element is turned off and the second switching element is turned on during the first mode, a second current flows along the first diode element, the bearing coil, and the second switching element. a capacitor (Cbs) to store direct current power; a first switching element connected between one end of the capacitor (Cbs) and one end of the bearing coil; a first diode element connected between the other end of the capacitor (Cbs) and the one end of the bearing coil; a second diode element connected between the one end of the capacitor (Cbs) and the other end of the bearing coil; a second switching element connected between the other end of the capacitor (Cbs) and the other end of the bearing coil; and the bearing coil is connected between the first switching element and the first diode element and between the second diode element and the second switching element, wherein when the first switching element and the second switching element are turned on simultaneously during the second mode, a first current flows sequentially along the capacitor (Cbs), the first switching element, the bearing coil, and the second switching element, and wherein when the first switching element is turned off and the second switching element is turned on during the first mode, a second current flows along the first diode element, the bearing coil, and the second switching element.