A laser beam processing machine comprising a chuck table for holding a workpiece, a laser beam application device for applying a laser beam to the workpiece held on the chuck table, a processing-feed device for moving the chuck table and the laser beam application device relative to each other in a processing-feed direction (X-axis direction), and an indexing-feed device for moving the chuck table and the laser beam application device relative to each other in an indexing-feed direction (Y-axis direction) perpendicular to the processing-feed direction (X-axis direction), wherein the laser beam application device includes a laser oscillation device for oscillating a laser beam, a first acousto-optic deflection device for deflecting the optical axis of a laser beam oscillated by the laser beam oscillation device in the processing-feed direction (X-axis direction), and a second acousto-optic deflection device for deflecting the optical axis of a laser beam oscillated by the laser beam oscillation device in the indexing-feed direction (Y-axis direction).