A disc clamping device seeks to attain size reduction and simplification of the structure without spoiling the smoothness of centering a disc. A disc clamper has an upwardly projecting central hung pin penetrating a circular hole formed in a clamp support member and having a head greater in diameter than the circular hole. At least either one of the portions of the edge of the circular hole and the head of the hung pin in engagement with each other is formed with a tapered surface for centering the disc clamper. The clamp support member is provided with an elastic member, for instance a leaf spring, for pushing the head against the edge of the circular hole.