An angle inclining structure for a desk contains a body and an angle inclining structure, the body including two opposite support legs, a horizontal rod, and two support posts connected with the two support legs and a first plate, wherein the angle inclining structure is disposed between the horizontal rod and the first plate and has a holder, a covering member, and a buffer member, the holder includes a locking tab and connects with the horizontal rod, a receiving room to receive a retainer and a pushing element, and a groove to receive a positioning member; the covering member includes a slot, plural tilted recesses, and a locking hole; a free end of the buffer member axially couples with one end of the covering member and a bottom surface of the first plate so that when the first plate axially rotates upwardly, the covering member slides on the holder.