The invention discloses a linear compressor of a plate spring supporting system adopting two different types of lines. The main assemblies thereof comprise four parts which are respectively a compressor assembly, a linear motor assembly, a piston assembly and a supporting system assembly. The compressor comprises a stand, a compressor shell, a compressor cylinder, an exhaust hole and a suction hole; the linear motor assembly comprises an inner yoke iron, an outer yoke iron, a permanent magnet, an anti-collision gasket, a coil framework and a coil on the upper surface thereof; a piston comprises a main piston shaft and a piston head; and a supporting system comprises two groups of plate spring groups with different types of line structures and a connecting frame. The structure has the characteristics that a spiral type plate spring supporting piston shaft assembly is adopted at one end with lighter mass of the piston head, and a spiral arm plate spring supporting piston head adopted at the end of the piston head moves in the cylinder to ensure clearance sealing; a linear arm plate spring is adopted at the rear end of the piston assembly to supply better support for the movement of the end with larger mass, the quantity of plate springs is reduced, and the volume of the compressor is saved.