A machine for making plug wraps for the tobacco industry, comprising: - an unwinding station configured to unwind a continuous web of wrapping material for the tobacco industry from a roll along a feed path, the continuous web having on one side a succession of equispaced additional elements; - a cutting station disposed along the feed path and configured to transversely cut the continuous web by making a succession of cuts at a predetermined position to obtain a succession of plug wraps, each comprising at least one additional element; - a detecting device disposed upstream of the cutting station and configured to detect the position of the additional elements along the feed path; - adjustment means for adjusting the feed path of the continuous web, disposed upstream of the cutting station and configured to modify the geometry of the feed path of the continuous web in such a way as to adjust the position of the continuous web, hence of the additional elements, along the feed path; - a control unit connected to the detecting device and to the adjustment means and acting on the adjustment means to set a variation in the feed path of the continuous web as a function of the position of each additional element detected by the detecting device; characterized in that it comprises: - an inspecting device, preferably an optical sensor, disposed downstream of the cutting station and configured to detect the position of the additional elements on the individual plug wraps, wherein the inspecting device is connected to the control unit, the control unit being configured to set a variation in the feed path of the continuous web as a function of the position of each additional element detected by the inspecting device. - an unwinding station configured to unwind a continuous web of wrapping material for the tobacco industry from a roll along a feed path, the continuous web having on one side a succession of equispaced additional elements; - a cutting station disposed along the feed path and configured to transversely cut the continuous web by making a succession of cuts at a predetermined position to obtain a succession of plug wraps, each comprising at least one additional element; - a detecting device disposed upstream of the cutting station and configured to detect the position of the additional elements along the feed path; - adjustment means for adjusting the feed path of the continuous web, disposed upstream of the cutting station and configured to modify the geometry of the feed path of the continuous web in such a way as to adjust the position of the continuous web, hence of the additional elements, along the feed path; - a control unit connected to the detecting device and to the adjustment means and acting on the adjustment means to set a variation in the feed path of the continuous web as a function of the position of each additional element detected by the detecting device; - an inspecting device, preferably an optical sensor, disposed downstream of the cutting station and configured to detect the position of the additional elements on the individual plug wraps, wherein the inspecting device is connected to the control unit, the control unit being configured to set a variation in the feed path of the continuous web as a function of the position of each additional element detected by the inspecting device.