A self-sealing pneumatic tire that has an inner surface provided with a layer of sealant and a plurality of edge strips that partially overlap the sealant layer to retain the sealant in position during construction and operation of the tire. Construction is simplified by utilizing a laminate structure incorporating such edge strips and also comprising an air impermeable elastomer strip, the center of which is coated with a layer of puncture sealant material and having the edge strips adhesively attached to the elastomer strip and partially overlapping the edges of the sealant layer. Also, a method of constructing this tire by attaching a tire body or carcass to this laminate structure prior to molding and curing the tire. During the molding process, the edge strips that partially overlap the sealant layer hold the sealant in place preventing it from flowing in an uncontrolled manner.