An apparatus and method for controlling an operation of a reciprocating compressor are disclosed in which a point of inflection with respect to an operation frequency of the reciprocating compressor is detected at a point of time when a phase difference between current and stroke is uniformly maintained, and an operation of the reciprocating compressor is controlled upon recognizing the detected point of inflection with respect to the operation frequency as a point TDC=O. The apparatus for controlling an operation of a reciprocating compressor includes: a control unit for detecting a phase difference between current and stroke and outputting a frequency inflection point detect signal or a frequency variable signal; and a stroke reference value control unit for determining whether a frequency inflection point has been detected or not according to the frequency inflection point detect signal and outputting a stroke reference value control signal based on the determining result.