An apparatus and method for controlling the operation of a reciprocating compressor are capable of preventing distortion of a current applied to the reciprocating compressor by generating a current amplitude value for compensating a difference value between a stroke reference value of the reciprocating compressor and a stroke estimate value and outputting the current amplitude value in a form of a sine wave to the reciprocating compressor. The apparatus for controlling an operation of a reciprocating compressor generates a current amplitude value for compensating a difference value between a stroke reference value and a stroke estimate value of the reciprocating compressor and outputs the current amplitude value in a sine wave form to the reciprocating compressor.