A linear compressor with a pumping chamber, in which a piston moves back and forth, and a frame, fixed to the pumping chamber, on which an oscillating body, connected to the piston, is fixed by at least one spring such as to move back and forth and provided with at least one electromagnet, for driving the back and forth movement of the oscillating body. A one-piece spring connects the oscillating body to the frame and the frame to a fixing body, for fixing the linear compressor to a support.