An apparatus is arranged to feed dampening water in an offset printing press. The apparatus comprises a plurality of spray nozzles (2) arranged in a row in a direction. Each of the nozzles includes an outlet formed therein for spraying the dampening water. The outlet has a cross section elongated in the direction in which the nozzles are arranged in the row, to spray the dampening water in an increasing fan-shaped area (14) defined in the direction in which the nozzles are arranged in the row. The apparatus further comprises baffle means (24) disposed at least on the opposite sides of each of the nozzles in the direction in which the nozzles are arranged in the row, to baffle air stream (22) from being directed toward the nozzle when spraying and stopping the dampening water.