The vascular graft is located within a lumen of a vessel. The vascular graft includes a tubular structure and an attachment ring connected thereto. A stent attachment structure is connected to the attachment ring. The stent attachment structure is connected to an inner surface of the vessel to secure the location of the vascular graft within the lumen. The vascular graft is made according to a method in which the end of the tubular structure is folded over the attachment ring. Alternatively, the vascular graft has circumferential slits near the end thereof. Strap structures extend through the slits and are folded for connection to the stent attachment structure. The vascular graft is made according to a method in which the strap structures are inserted through the slits and folded for connection to the stent attachment structure.
