A controller for three-dimensional laser beam machine having a head structure in which the machining point is unchangeable even when the rotation axis and posture axis are rotated, wherein the end position and posture of the nozzle are taught, and the machining is effected according to the teaching. The control is such that the nozzle-direction vector is calculated from the current angles of the rotation axis (14) and posture axis (16), the angle by which the posture axis (16) changes for a certain time is calculated, the angle by which the rotation axis (14) is rotated according to a change of the angle of the posture axis (16) in such a way that the X and Y directions of the nozzle-direction vector is kept unchanged, and the rotation axis (14) is made to rotate by the calculated angle.