A laser beam machining head includes a dividing optical system for dividing laser light into two separate laser beams, and providing spacing therebetween; a condensing optical system for condensing the separate laser beams into condensed laser light, and projecting it onto a cutting site of an object to be cut; and an inner assist gas nozzle placed between the separate laser beams, a width of an opening of a tip portion of the inner assist gas nozzle being nearly equal to a cutting width. Or the tip opening of the inner assist gas nozzle is slender; or its tip side is inclined, and the angle of inclination is variable; or the relative positions of the inner assist gas nozzle and a workpiece, or the relative positions of the focal position of the condensing optical system and the workpiece are variable independently; or an outer assist gas nozzle surrounding the separate laser beams is provided.