An apparatus and a method for laser machining with a gap or tracing control, capable of shortening time required for moving a machining head from a machining end point (A) of one machining shape (S1) to a machining start point (D) of a next machining shape (S2). The laser machining is performed with gap or tracing control in which a gap amount between the machining nozzle and the workpiece is controlled to be constant. Driving of a Z-axis is started at a predetermined velocity when the machining nozzle reaches a machining end point (A) of one machining shape. In the drive of the Z-axis, when the Z-axis is driven by a predetermined amount (a), driving of an X-axis and a Y-axis is started so that the machining nozzle moves to the next machining start point (D) by rapid traverse. A direction of driving of the Z-axis is reversed at a middle point (C) between the machining end point (A) and the machining start point (D). Alternatively, driving of the Z-axis may be discontinued at a different retreated point. When the gap amount reaches a predetermined amount (d), the gap control is started. A length of the motion path from the machining end point (A) to the machining start point (D) is made shorter, and frequency of stopping/switching operation of the gap control axis and the machining feed axes is reduced, to shorten the time required for the transition to the machining start point (D) of the next machining shape (S2).