A laser beam machine executes a cutting operation by irradiating a laser beam onto a workpiece. The cutting operation of nonferrous metals having a considerable thickness is executed effectively and stably. A piercing operation is executed at point A under machining condition A, forming an arc-shaped portion. Then, the machining condition A is changed to machining condition B to execute an enlargement processing, and the arc-shaped portion is extended as it is, forming an enlarged cutting groove. After the enlargement processing is completed at point B, the standoff (or distance from the tip end of a machining nozzle to the surface of the workpiece) is set to as short a distance as possible, and the machining condition is modified to machining condition C. Thus, a cutting operation is started according to machining condition C. Therefore, the cutting operation is executed in substantially the same state as that in which a cutting operation is started directly from the outer-side end of the workpiece. In addition, in the case where the cutting operation is executed, the assist gas pressure is set to a high value, and the standoff is set to a low value, so that dross scattering effect by the assist gas appears more remarkably. Thus, the cutting operation is executed effectively and stably.