Abstract: A cover is woven into a cylindrical shape with many warp yarns composed of a hydrophilic fiber and with one or several weft yarns composed of a hydrophilic fiber with a water shrinkage about 10 to 40%. This cover has a quality of rapid response for controlling the moisturizing condition of the printing surface which is designated by the difference in the weight of the cloth of the cover between a wetted condition in which the cover absorbs and stores enough water without dropping and a dry condition in which the cover is treated with a centrifugal dehydrator for 10 minutes after being wetted. The warp and weft yarns are of less than 220 denier and have a density of 20 threads per centimeter. The weight of the cloth of the cover is less than 200 g/m.sup.2 and the thickness is less than 0.5 mm.