The present invention relates to a disc chucking apparatus having claws that horizontally move and provide elasticity to improve performance in centering and chucking a disc. The disc chucking apparatus includes: a centering base to which an inner circumferential surface of a disc is fixed; a plurality of chuck chips arranged at regular intervals along an outer circumferential surface of the centering base; and a plurality of elastic support parts disposed to be opposite to the chuck chips on the centering base, rotating horizontally when the disc is mounted, and pressing the inner circumferential surface of the disc in an outer diameter direction thereof.