An apparatus for mounting a compressor comprises: a bracket installed at one surface of a compressor and having a plurality of holes; a plurality of supporting members extending from a base on which the compressor is mounted and protrudingly formed to pass the holes of the bracket; and a plurality of elastic members, each elastic member surrounding one end of each supporting member and inserted in the hole at a certain interval between its inner circumferential surface and the supporting member, for elastically supporting the bracket, thereby effectively reducing vibration of the compressor and improving reliability of a product provided with the compressor.