Cooling water is sprayed under a predetermined pressure range and at a predetermined discharge rate over the both surfaces of a sheet to be treated which is reciprocated lengthwise at such a velocity that the product of the reciprocating velocity and thickness of the sheet may be maintained within a predetermined range. The spraying direction of each spray nozzle is individually controlled so that any water remaining over the surface of the sheet may be expelled out. The method and apparatus is especially adapted for use in the normalizing process and in the process for cooling hot-rolled sheet steel.