A discharge valve apparatus for a reciprocating compressor comprises a discharge cover having built-in volume so as to cover a front end surface of the cylinder; a discharge valve disposed so as to be contacted/separated to/from the front end surface of the cylinder by a piston which undergoes a reciprocating movement inside the cylinder; and a valve spring having both ends respectively adhered to rear side of the discharge valve and to inner surface of the discharge cover so as to elastically support the rear side of the discharge valve. A rotation radius of the valve spring of a conical type is formed to be gradually reduced or increased so that impacts of a part to other parts during the compression can be prevented. Accordingly, when the valve spring is compressed in accordance with the compression and discharge strokes of the piston, the impacting noise caused by the impacts of the respective parts in the valve spring can be prevented previously.