A laser robot having a height sensing device (13) arranged at a position very close to a laser-beam projecting machining head (9) so that the axis of the height-sensing device (13) is parallel to the longitudinal axis of the machining head (9), the three-dimensional distance data representing the positional relationship between the laser projecting nozzle (9a) of the machining head (9) and the measuring end (13a) of the height-sensing device (13) being stored in advance in the robot controller (10), the longitudinal distance between the height-sensing device (13) and a starting point of laser-beam machining being automatically measured from directly above the starting point, and a longitudinal distance between the laser beam projecting nozzle (9a) of the machining head (9) and the machining starting point being corrected on the basis of the three-dimensional distance data and the longitudinal distance measured by the height sensing device (13) to thereby accurately locate the machining head at a position corresponding to the starting point for the laser machining operation.