To remove components such as BOD, COD, normal hexane equivalent value SS or the like in damping water to recycle the damping water without discarding the same.

A line pump 4 for forcibly circulating damping water, a potential attraction filter device 2 utilizing attraction action of zeta potential and an activated carbon filter device 3 utilizing the adsorbing action of activated carbon are successively arranged on the way of the circulating passages 9a-9d connected to the water shoe 12 of the damping part of an offset rotary press by connection passages 10a, 10b and introducing damping water in the water shoe 2 form an inlet port 8a and leading the damping water out of a lead-out port 8b to circulate the same. The fine particle components such as ink, paper powder or oil contained in damping water are attracted and removed by the potential attraction filter device 2 and damping water is decolored and deodorized by the activated carbon filter device.