To control cutting process with cutting quality to obtain product without any uncut portion on a corner portion, and to respond to a change in cutting speed. Water jet cutting performed by: inputting a cutting program, set cutting speed, cutting parameters; calculating cutting speed matching the cutting quality; calculating cutting shape from the cutting program and dividing the cutting shape into a linear portion and a corner portion; calculating a corner cutting speed for the corner portion on the basis of a shape of the corner portion within range from the calculation cutting speed to the set cutting speed, set cutting speed equal to or higher than the calculation cutting speed; set cutting speed and the corner cutting speed to the linear portion and the corner portion, respectively, in the cutting program; moving the nozzle relative to the workpiece on the basis of the cutting program assigned with cutting speeds.