A stator fixing apparatus of a reciprocating compressor comprises a first frame on which a plurality of first core blocks, each comprising a plurality of laminated stator core sheets, are radially coupled, the plurality of first core blocks being coupled to one side surface of a bobbin body, and a second frame on which a plurality of second core blocks, each comprising a plurality of laminated stator core sheets, are radially coupled. The plurality of second core blocks are coupled to the other side surface of the bobbin body. A coupling portion is provided at each contact portion between the first core block and the second core block, for coupling the first and second core blocks. Thus, deformation of an initial shape of the stator or increase of a defect rate due to a molding material can be prevented, and heat and moisture can easily be discharged, so as to improve the efficiency and reliability of the reciprocating compressor.