Abstract: A grate cooler of simple construction whose cooling grate is substantly protected against wear and which can be operated in simple fashion and with a high cooling efficiency. A plurality of rotatably supported tubular oscillating shafts, spaced apart from one another, are arranged transversely to the conveyance direction of cooling feed material above a stationary cooling grate. Upwardly extending shovel arms (16a, 16b, 16c), are attached to the shafts which move with a reciprocating oscillatory motion (17) in the conveyance direction of cooling feed material. The shovel arms have a pushing surface on their forward side and a wedge surface on their rearward side and, in their oscillatory motion, moving the hot bed of cooling feed material successively from the beginning of grate-cooler to the discharge of the grate cooler.