There is disclosed a method of feeding a dampening water to a plate cylinder in an offset printing press which is accelerated to, operated at and then decelerated from a predetermined speed for printing. The method comprises the step of programmatically controlling the feeding amount of the dampening water to increase in accordance with the increase in speed of the printing press along a first curve which is predetermined to indicate the relation of the feeding amount of dampening water to the speed of printing press, when the printing press is accelerated. The method further comprises the step of programmatically controlling the feeding amount of the dampening water to decrease in accordance with the decrease in speed of the printing press along a second curve which is predetermined to indicate the relation of the feeding amount of dampening water to the speed of printing press, when the printing press is decelerated. The first and second curves being different in feeding amount of the dampening water from each other.