A laser beam processing machine comprising a chuck table for holding a workpiece, a laser beam application means for applying a laser beam to the workpiece held on the chuck table, a processing feed means for moving the chuck table and the laser beam application means relative to each other in a processing-feed direction and an indexing-feed means for moving the chuck table and the laser beam application means in an indexing-feed direction perpendicular to the processing-feed direction, wherein the laser beam application means comprises a first laser beam application means for applying a first pulse laser beam having an energy density per one pulse of 20 to 60 J/cm2 and a second laser beam application means for applying a second pulse laser beam having an energy density per one pulse of 3 to 20 J/cm2.