An apparatus for controlling an operation of a compressor includes: a back electromotive force calculator for calculating a back electromotive force of a compressor based on a value of a current applied to a motor of the compressor and a value of a voltage applied to the motor of the compressor; an operation frequency reference value determining unit for detecting a mechanical resonance frequency of the compressor based on the back electromotive force value and the current value and determining the detected mechanical resonance frequency as an operation frequency reference value; and a controller for varying an operation frequency of the compressor according to the determined operation frequency reference value.