A clamp changing apparatus includes a holder (70) including a plurality of clamp-holding devices (72), each of which holding a clamp (10) thereon, a robot (50) including a shaft (501), and a coupling device (30) secured on the shaft of the robot. The robot selects one of the clamps held on the clamp-holding devices according to a predetermined machining program therein, changes out a used clamp for the selected clamp, and mounts the selected clamp on the coupling device.