An apparatus and method are disclosed to control an operation of a reciprocating compressor capable of precisely controlling an operation (stroke) of a reciprocating compressor regardless of a parameter of an internal motor of the reciprocating compressor and a mechanical error of the reciprocating compressor. The apparatus for controlling an operation of a reciprocating compressor which determines a stroke estimate value corresponding to a point when a discharge valve of the reciprocating compressor is opened as a stroke reference value, and controls a voltage applied to the reciprocating compressor according to the determined stroke reference value.