Alaser cutting device comprising a laser oscillator, a transmission fiber, a laser machining head and a laser machining robot, said laser cutting device being configured to cut a work by emitting a laser beam output from the laser oscillator onto the work via the transmission fiber and the laser machining head fitted to a front end of the laser machining robot, the laser cutting device comprising: a control unit that controls operations of the laser machining robot and the laser oscillator, wherein the laser machining robot has a predetermined speed range in which the laser machining robot is allowed to move with a given tracking accuracy, and a usable range of a cutting speed of cutting the work is set based on the speed range, wherein the control unit includes a memory storing a plurality of machining condition tables carrying data on cutting conditions, wherein each of the machining condition tables includes, as parameters associated with a material and a plate thickness of the work, at least a laser oscillation frequency, a laser power output, a laser power output duty, the usable range of the cutting speed, an effective range demarcated by the cutting speed and the laser power output that are set so that a cut surface of the work meets given finishing conditions, and an approximation of a lower boundary of the effective range, and wherein the control unit selects a machining condition table from the plurality of machining condition tables stored in the memory so that the cutting speed of cutting the work and the laser power output meet given conditions, and controls operations of the laser machining robot and the laser oscillator so that the work is cut based on the selected machining condition table, characterized in that said control unit is configured such that when an extent of an overlap between the effective range and the usable range of the cutting speed, the effective range and the usable range being included in the selected machining condition table, is smaller than a given range, at least either of the laser oscillation frequency and the laser power output duty is changed, and the machining condition table is selected again so that the extent of the overlap between the effective range and the usable range of the cutting speed becomes equal to or larger than the given range, and wherein the control unit controls operations of the laser machining robot and the laser oscillator so that the work is cut based on the machining condition table selected again. a control unit that controls operations of the laser machining robot and the laser oscillator, wherein the laser machining robot has a predetermined speed range in which the laser machining robot is allowed to move with a given tracking accuracy, and a usable range of a cutting speed of cutting the work is set based on the speed range, wherein the control unit includes a memory storing a plurality of machining condition tables carrying data on cutting conditions, wherein each of the machining condition tables includes, as parameters associated with a material and a plate thickness of the work, at least a laser oscillation frequency, a laser power output, a laser power output duty, the usable range of the cutting speed, an effective range demarcated by the cutting speed and the laser power output that are set so that a cut surface of the work meets given finishing conditions, and an approximation of a lower boundary of the effective range, and wherein the control unit selects a machining condition table from the plurality of machining condition tables stored in the memory so that the cutting speed of cutting the work and the laser power output meet given conditions, and controls operations of the laser machining robot and the laser oscillator so that the work is cut based on the selected machining condition table, characterized in that said control unit is configured such that when an extent of an overlap between the effective range and the usable range of the cutting speed, the effective range and the usable range being included in the selected machining condition table, is smaller than a given range, at least either of the laser oscillation frequency and the laser power output duty is changed, and the machining condition table is selected again so that the extent of the overlap between the effective range and the usable range of the cutting speed becomes equal to or larger than the given range, and wherein the control unit controls operations of the laser machining robot and the laser oscillator so that the work is cut based on the machining condition table selected again.