Provided is an angle tool holder installed on an attachment which is mounted on a spindle head of a vertical machining center and retains the angle tool holder, thereby permitting 5-face machining. The angle tool holder, the whole of which is represented by a symbol (500), comprises a shank (510) which is inserted into a main spindle of the vertical machining center. Rotation of the shank (510) drives an angle cutter (520) in such way that the direction of the pertinent drive shaft is changed perpendicularly via a gear transmission mechanism or the like in a housing (540). An arm (550) connected to the housing (540) is provided with three pull stud bolts (570). The three pull stud bolts (570) are disposed at intervals of 90 degrees and are simultaneously clamped by three of four collet chucks disposed in a 5-face machining attachment unit.