A dampening arrangement for a printing press such as a lithographic press includes at least one solution receiving roller for receiving dampening solution and other rollers for conveying the dampening solution to a printing plate. The dampening arrangement is provided with a nozzle unit having a plurality of nozzles arranged substantially in parallel with the axis of the solution receiving roller and opposed to predetermined areas on the surface of the solution receiving roller, and a dampening solution supply source connected to the nozzle means for supplying the nozzles with a pressurized dampening solution. The distance between the nozzles and the surface of the solution receiving roller is automatically adjusted in accordance with the printing speed of the printing press. The printing press does not cause a printing defect due to excess supply of the dampening solution even when the printing press is operated at a high speed.