A tapered tendon graft anchor employed during a tendon graft reconstruction surgical procedure. The anchor of the invention comprises a "hair-pin" configuration formed of a loop and two opposing leafs. Each of the leafs include inwardly extending teeth in facing alignment with each other. The outer surfaces of the leafs are tapered to a frustro-conical shape. A harvested tendon with a bone block at one end is positioned with a cavity defined by the loop of the "hair pin" configuration with the tendon positioned between the inwardly extending teeth of the leafs. When the anchor is positioned within a hole in the bone of the joint whose ligament is to be reconstructed, the tendon is tightly grasped by the anchor to securely anchor the tendon in the hole allowing the bone block to be grafted within the hole.