A linear compressor driving apparatus having an inverter which supplies a driving current of a predetermined frequency to a linear compressor. The linear compressor driving apparatus further includes an inverter controller for controlling the inverter on the basis of resonance frequency information so that the frequency of an output current from the inverter becomes equal to the resonance frequency, and instantaneous values of an output current and an output voltage from the inverter are measured at a phase timing in which an amount of change in the output current of the inverter becomes zero. A piston stroke is calculated from these measured values. In such a linear compressor driving apparatus, a stroke and a top clearance of the piston of the linear compressor can be accurately detected by relatively simple arithmetic processing without using a position sensor.