The present invention discloses an oil supply apparatus of a linear compressor. In the linear compressor including a main body frame, a cylinder installed on the main body frame, and a piston installed inside the cylinder, for performing linear reciprocation, the oil supply apparatus circulates the oil between the cylinder and the piston. The oil supply apparatus of the linear compressor includes an oil supply passage for supplying the oil to a gap between the cylinder and the piston, and an oil pumping means consisting of an oil cylinder fixed to the main body frame to communicate with the oil supply passage, a mass member installed in the oil cylinder and linearly reciprocated by vibration of the main body frame, for pumping the oil, and oil elastic members installed in the oil cylinder, for elastically supporting the mass member at both sides of the mass member. A mass of the mass member and elastic moduli of the oil elastic members are set so that a natural frequency by the mass of the mass member and the elastic moduli of the oil elastic members can be smaller than an operating frequency of the main body frame.