A retainer assembling apparatus which assembles a retainer to a valve stem via a cotter which engages with an engaging groove formed on the valve stem, the cotter comprising a pair of cotter segments, said apparatus comprising: a cylindrical body including a lower end which the retainer attached with the cotter is brought into contact with, said cylindrical body allowing the valve stem to enter from the lower end; a holding portion which holds the retainer contacting the lower end of the cylindrical body; a push-up shaft which enters from a lower end of the retainer held by said holding portion and pushes up the pair of cotter segments into the cylindrical body; and an axial body which is arranged in said cylindrical body to be coaxial with said push-up shaft and to be coaxially movable; wherein said cylindrical body includes a tapered inner circumferential portion which is formed into a tapered shape, a diameter of which is increased upward, on an inner circumferential wall lower portion thereof; and wherein said apparatus further comprises a cylindrical contact member which is mounted around said axial body and which is arranged in said cylindrical body to be freely movable in an axial direction of said axial body; characterized in that said cylindrical contact member contacts inner edge portions of said pair of cotter segments from a position above the cotter segments; and in that said apparatus further comprises: a cylindrical tapping member which includes an insertion hole through which said axial body is inserted, and is arranged in said cylindrical body to be movable in the axial direction of said axial body; and a driving unit which moves said tapping member to tap said contact member downward in the axial direction of said axial body. a cylindrical body including a lower end which the retainer attached with the cotter is brought into contact with, said cylindrical body allowing the valve stem to enter from the lower end; a holding portion which holds the retainer contacting the lower end of the cylindrical body; a push-up shaft which enters from a lower end of the retainer held by said holding portion and pushes up the pair of cotter segments into the cylindrical body; and an axial body which is arranged in said cylindrical body to be coaxial with said push-up shaft and to be coaxially movable; wherein said cylindrical body includes a tapered inner circumferential portion which is formed into a tapered shape, a diameter of which is increased upward, on an inner circumferential wall lower portion thereof; and wherein said apparatus further comprises a cylindrical contact member which is mounted around said axial body and which is arranged in said cylindrical body to be freely movable in an axial direction of said axial body; characterized in that said cylindrical contact member contacts inner edge portions of said pair of cotter segments from a position above the cotter segments; and in that said apparatus further comprises: a cylindrical tapping member which includes an insertion hole through which said axial body is inserted, and is arranged in said cylindrical body to be movable in the axial direction of said axial body; and a driving unit which moves said tapping member to tap said contact member downward in the axial direction of said axial body.