The present invention relates to a compressor. In one aspect of the present invention, a compressor is provided, including a cylinder having a compression chamber, a valve assembly mounted on one open end of the cylinder, and a head assembly on the valve assembly. The head assembly includes a suction muffler, a head plate, a head cover, a damping pipe, and a discharge muffler. The suction muffler includes at least one wing on an outside surface of an outlet part thereof, and the head plate includes a first cut away part for inserting the wing of the outlet part. The head cover is closed fastened to the head plate so as to press down the suction muffler. In the meantime, the head plate includes a recess for inserting the middle part of the damping pipe therein to hold the damping pipe, and the discharge muffler is fitted to one surface of the head plate to surround the damping pipe.