A valve fastening structure of a reciprocating compressor is provided. The valve fastening structure of the reciprocating compressor includes a piston, which is combined with a moving magnet of a driving motor and is in a linear reciprocating motion inside a cylinder and in which a refrigerant channel is formed in the direction of the reciprocating motion, a suction valve arranged in the leading end of the piston, the suction valve for opening and shutting the refrigerant channel of the piston, and magnets inserted into and fixed to the leading end of the piston, the magnets for fixing the suction valve by magnetic force. It is possible to minimize dead volume in the cylinder and to easily control the stroke of the piston by establishing the suction valve as the cardinal point during the controlling of the stroke of the piston. Accordingly, the efficiency of the compressor is improved. Also, it is possible to improve the reliability of the compressor by preventing the suction valve from being deteriorated when the suction valve is used for a long time or preventing the suction valve from being damaged by excessive suction pressure.