A compact, accurate, and inexpensive laser beam machine combining the simple structure of a two-dimensional stepping motor and features of laser-beam machining. The machine has a rotating shaft (39) capable of rotating about a vertical axis. The shaft (39) is mounted on a frame (61). A mirror (52) which reflects laser beam emitted from a laser is mounted on the shaft. The stepping motor has a mover (20). A second rotating shaft (34) capable of rotating about a vertical axis is mounted on the mover (20). A mirror (51) which reflects the laser beam, reflected by the mirror (52) toward a workpiece, is mounted on the second shaft (34). The rotating shafts (34, 39) are so driven that if the mover (20) shifts, the laser beam is kept focused to the workpiece by the two reflecting mirrors.