An apparatus and method for controlling an operation of a linear compressor by detecting a phase difference inflection point at a time point when a phase difference between a current and a stroke is placed within a certain region, and by recognizing the phase difference infection point as a top dead center (TDC)=O. The apparatus for controlling an operation of a linear compressor, comprises: a controlling unit for detecting a phase difference between a current and a stroke, and outputting a frequency varying signal or a phase difference inflection point detecting signal based on the detected phase difference; a phase difference inflection point detecting unit for judging whether to detect a phase difference inflection point or not by the phase difference inflection point detecting signal, and outputting a stroke command value controlling signal based on a result of the judgement; and a stroke command value determining unit for determining a stroke command value based on the stroke command value controlling signal.