To provide a thermal cutting machine which with a cut piece for example rising and interposing between one part and another to be machined in a workpiece, can suppress interference of the cut piece with a laser machining head.

In an idle moving process in which a laser machining head 25 is transferred at an idle moving speed faster than the cutting speed, the gain of a controller 37 in the upward retreating of the laser machining head 25 is designed to be higher than the normal gain of the controller 37 in the laser cutting process.