To provide an ink smoothing roller of an offset rotary press for producing a printed product of high quality by cooling controlling a nip pressure between a mixing roller and a form roller and a heat generated due to a lateral movement of the smoothing roller, suppressing a heat transfer from a printer body driver to a low value, holding a temperature of a surface of the roller constant and holding flowability of the ink constant.

The ink smoothing roller comprises a first stepped shaft made of a low thermal conductivity member having a through hole for passing a cooling water, a second stepped shaft made of the low thermal conductivity member to mount a rotating and lateral moving means, and a roller steel tube shrink fit molded with the two stepped shafts.