Disclosed is a hot-pressing apparatus capable of quenching a workpiece at a sufficient cooling rate. A hot-pressing apparatus includes a lower die and an upper die. The hot-pressing apparatus causes the dies to press a workpiece, and at the same time, to keep the forming surfaces thereof in contact with the workpiece to cool the workpiece. Depression parts are formed in parts of the lower die which faces external corners of the upper die, and parts of the upper die which faces external corners of the lower die. The water-feed channel and the lower water-feed device, and the water-feed channel and the upper water-feed device are provided to feed cooling water to spaces between the workpiece and the dies.