A stent delivery catheter includes at least an inner and outer body, and a specially shaped balloon affixed near one end of both of the inner and outer bodies. At least the outer body is tubular, and the space between the outer and inner bodies defines an inflation lumen for inflating and deflating the balloon. The balloon is designed to surround and hold a compressed self-expanding stent in a small initial size. An inner portion of the cylindrical balloon extends from where it is affixed to the inner body of the catheter shaft at a point proximal to the stent to a distal leading edge at a point distal to the stent. At this leading edge, the balloon is folded back upon itself, and an outer portion of the balloon extends proximally from the leading edge to a point proximal of the stent where it is affixed to the outer body of the catheter shaft. When the outer body is retracted in the proximal direction, the balloon progressively peels back or everts, to progressively release the stent. This peeling action minimizes any friction that may exist between the stent and balloon during stent deployment. The leading distal folded edge of the balloon, both inner and outer portions, are tapered inward. This inner and outer tapering of the balloon portions tends to protect the leading edge of the stent, provides for easier advancement of the catheter system along the desired body passageway for treatment, and minimizes friction as the balloon is retracted or peeled back upon itself.