To prevent water due to dew condensation from dropping to a heat insulating material provided around a water tank.

A heat insulating material 2 for keeping dampening water warm is provided in the outer surface of the water tank 1 storing the dampening water. A water absorbing member 3 having water retentivity is arranged around the heat insulating material 2. In other words, even when the outer surface of the heat insulating material 2 has dew condensation, the water due to the dew condensation is absorbed and held by the water absorbing member 3. Therefore, the drop of the water due to the dew condensation to the heat insulating material 2 can be prevented. As a result, failures caused by the drop of the water due to the dew condensation, that is, such a situation that the metal part of an offset printer is rusted or a web is contaminated can be prevented.