When an operation is performed in a direction (Z-axis direction) in which a machining head is brought closer to workpiece, a numerical controller that controls a laser beam machine avoids a collision of the machining head with the workpiece by switching to gap control when a gap sensor detects a gap amount between the machining head and the workpiece. At this point, whether to perform the operation to bring the machining head closer to the workpiece by gap control using a detection value of the gap sensor or by moving the machining head to a position determined by parameters can be selected using a mode switching unit.