A device for connecting a trailing end of a previously drawn-out web from a first web roll to a leading end portion of a newly drawn-out web from a second web roll has a vertical guide unit, a drawing-out unit, a feeding unit, an adhesive tape supplying unit and cutting members. The previously drawn-out web which is running vertically downward is guided by the vertical guide unit. The leading end portion of a web is drawn out from a new web roll by the drawing-out unit and moved vertically downward by the feeding unit in the vicinity of and along the previously drawn-out web. An adhesive tape is attached to the leading end portion of the newly drawn-out web by the adhesive tape supplying unit. The leading end of the newly drawn-out web is connected to the trailing end of the previously drawn-out web by the adhesive tape. After the previously and newly drawn-out webs have been connected together, the excess portions of both webs are removed by the cutting members.