An apparatus and method for controlling an operation of a compressor are disclosed to enhance a compressor efficiency in each operation mode in operating a compressor in a power mode or power saving mode according to an external load. The apparatus for controlling an operation of a compressor, including: a controller that generates a control signal to select an operation mode of the compressor according to an operation load of the compressor; a compressor motor that includes a main coil and a sub-coil and is driven in one of a plurality of operation modes according to a control signal of the controller; and a power supply unit that applies power via capacitors each having a different capacitance to the sub-coil of the compressor motor according to a control signal of the controller.