A metal-sheet quenching apparatus cools a metal sheet while conveying the metal sheet and includes a cooling tank in which a cooling fluid is to be stored and the metal sheet is immersed in the cooling fluid to be cooled; restraining rolls that are installed inside the cooling tank and convey the metal sheet that has been cooled in the cooling tank while restraining the metal sheet in the thickness direction; a water-level adjustor that adjusts the height of a fluid surface of the cooling fluid inside the cooling tank; and a position control device that adjusts the height of the fluid surface of the cooling fluid inside the cooling tank by controlling the operation of the water-level adjustor.