An apparatus and a method for controlling an operation of a reciprocating compressor which can improve operational efficiency of the reciprocating compressor are provided. The apparatus for controlling the operation of the reciprocating compressor includes a resonance frequency operation unit for calculating a mechanical resonance frequency of the reciprocating compressor, an operating frequency reference value generation unit for comparing the calculated mechanical resonance frequency with a current operating frequency of the reciprocating compressor, and generating an operating frequency reference value according to the comparison result, and a controller for controlling a motor of the reciprocating compressor according to the generated operating frequency reference value.