To provide a head which has the high precision of cutting and machines the cutting face suitably, in the head of a laser beam machines spouting an oxygen gas etc. at the same time of irradiating a laser beam.

A taper cylinder 11 having a taper face of a small inside diameter of the lower end side is installed inside the cylinder attached with a lens 10 in order to converge the laser beam, the upper end of the taper cylinder 11 is extended near the lens and on the lower end is installed with a head tip 3. The oxygen gas, etc., flowing between a cylinder 6 and the taper cylinder 11 is struck on the lens face and flows inside the taper cylinder 11.