A glass door hinge structure is installed on a lateral side of a glass door, and the glass door is combined with a hinge body, a hinge cover, an axial bolt and a fixing base, and the fixing base is fixed on the edge of a doorway. The hinge body is a thickened face portion, and the hinge cover has a protrusion attached onto an internal surface of the hinge cover, and the protrusion is in form of an indent, and both sides of the indent separately have a penetrating hole for installing the axial bolt, and the upper and lower positions of the thickened face portion have two transversally disposed screw thread holes and penetrated through the inner edge of the penetrating hole for an interconnection. A right-angled concavely cut plane is disposed on both upper and lower positions on the same side of the axial bolt, such that when the axial bolt is passed through the hinge body and the fixing base and the long screw bolt outside the hinge body is screwed into the screw thread hole and to a limit position on the concavely cut plane of the axial bolt of the penetrating hole. Finally, the glass door and hinge cover are installed, and the long screw bolt is turned to adjust the angle of the glass door and align the glass door evenly with the doorway. The invention also can enhance the screw connection and use of the long screw bolt and prevent it from being damaged easily.