A linear compressor, comprising: a cylinder having a compression space therein; a piston linearly reciprocated in the cylinder to compress a refrigerant sucked into the compression space; one or more springs (8a, 8b) provided to elastically support the piston in the motion direction of the piston; a motor connected to the piston to linearly reciprocate the piston; and a control apparatus comprising: a coil winding body laminated on the motor, a capacitor connected in series to the coil winding body, a constant power supply unit for receiving external power, converting the external power into a specific size of constant power with at least one between constant voltage or the constant frequency, and applying the constant power to the capacity and the coil winding body; and a control unit for inducing an output change of the linear compressor according to a load, by controlling the constant power supply unit to supply the specific size of constant power to the capacity and the coil winding body, wherein the motor can automatically change the output of the piston according to the load, characterized in that the coil winding body and the capacitor are configured such that the circuit operating frequency is equalized to a natural frequency in the overload operation, wherein the natural frequency is estimated by the mechanical spring constant, the gas spring constant and a mass of the piston. a cylinder having a compression space therein; a piston linearly reciprocated in the cylinder to compress a refrigerant sucked into the compression space; one or more springs (8a, 8b) provided to elastically support the piston in the motion direction of the piston; a motor connected to the piston to linearly reciprocate the piston; and a control apparatus comprising: a coil winding body laminated on the motor, a capacitor connected in series to the coil winding body, a constant power supply unit for receiving external power, converting the external power into a specific size of constant power with at least one between constant voltage or the constant frequency, and applying the constant power to the capacity and the coil winding body; and a control unit for inducing an output change of the linear compressor according to a load, by controlling the constant power supply unit to supply the specific size of constant power to the capacity and the coil winding body, wherein the motor can automatically change the output of the piston according to the load, a coil winding body laminated on the motor, a capacitor connected in series to the coil winding body, a constant power supply unit for receiving external power, converting the external power into a specific size of constant power with at least one between constant voltage or the constant frequency, and applying the constant power to the capacity and the coil winding body; and a control unit for inducing an output change of the linear compressor according to a load, by controlling the constant power supply unit to supply the specific size of constant power to the capacity and the coil winding body, wherein the motor can automatically change the output of the piston according to the load, characterized in that the coil winding body and the capacitor are configured such that the circuit operating frequency is equalized to a natural frequency in the overload operation, wherein the natural frequency is estimated by the mechanical spring constant, the gas spring constant and a mass of the piston.