A dampening water amount regulating apparatus 40 includes a plurality of air supply boxes 41 disposed in a line in an axial direction of a water transfer roller 8 and each defines one air blowing portion. The air supply box 41 includes a substantially U-shaped air passage 67 that allows air in an air supply chamber 57 to pass along an outer peripheral surface of the water transfer roller 8 and supplies the same into an air discharge chamber 60. A valve mechanism 44 that increases and decreases an air amount is provided at a midsection of the air passage 67.