To machine under an optimum condition a work which is likely to crack, for instance, in such a laser beam machining as a laser beam cutting or a laser beam welding, and to simultaneously perform a laser beam cutting and a chamfering.

The device is characterized by the fact that dichroic mirrors 5 and 25 are provided between plural laser oscillators 3A and 3B and a laser machining head 11 furnished with a single condenser lens 13 which radiates laser beams LB1 and LB2 toward a work W to be machined, the dichroic mirrors collect the laser beams LB1 and LB2 having different wave lengths outputted from the plural laser oscillators 3A and 3B onto an optical axis, and the collected laser beams LB1 and LB2 are converged upon a single condenser lens 13 provided on the laser beam machining head 11.