An apparatus for controlling an operation of a reciprocating compressor includes a voltage detecting unit for detecting a positive half-wave voltage of an AC voltage applied to a motor of the reciprocating compressor; a current detecting unit for detecting a positive half-wave current of the AC current passing through the motor; a voltage and current estimating unit for estimating a negative half-wave voltage of the AC voltage applied to the motor and a negative half-wave current of the AC current passing through the motor based on the detected positive half-wave voltage and the detected positive half-wave current; a stroke estimating unit for estimating a stroke of the reciprocating compressor based on the detected positive half-wave voltage and the detected positive half-wave current and the negative half-wave voltage and the negative half-wave current which have been estimated by the voltage and the current estimating unit; a stroke controller for outputting a stroke control signal of the reciprocating compressor based on a comparison value between the estimate stroke estimate value and a stroke reference value of the reciprocating compressor; and a power source unit for applying positive DC power to the voltage detecting unit and the current detecting unit.