Abstract: A laser beam machining apparatus capable of highly accurate machining at a high speed. A parallel link mechanism including a plurality of links is fixed to a frame and a workpiece holder having moving means is provided thereunder. The links of the parallel link mechanism connect a movable member with a stationary member, and the movable member is moved with respect to the stationary member by the extending/retracting operation of the links. A laser head serving as a machining head is attached to the movable member. A supply line includes a laser transmitting optical fiber, pipes for supplying water, assist gas, etc., and an electrical signal line. A laser beam LB outputted from the laser head performs machining on a workpiece W on the workpiece holder. The supply line passes through a through hole formed inside link joint portions on the stationary member. Hollow motors for driving the links of the parallel link mechanism are mounted on the stationary member.