A laser beam machining apparatus includes laser beam irradiation unit for irradiating a wafer held on a chuck table with a laser beam, and control unit. The laser beam irradiation unit includes a laser beam oscillator for oscillating a laser beam with such a wavelength as to be transmitted through said wafer, repetition frequency setting section for setting a repetition frequency of pulses in the laser beam oscillated from the laser beam oscillator. The control unit includes a memory for storing coordinates of an arcuate chamfer part formed at the outer periphery of the wafer and coordinates of a flat surface part surrounded by the chamfer part, and controls the repetition frequency setting section so as to set the repetition frequency of the pulses in the laser beam with which to irradiate the flat surface part to a value suitable for machining of the wafer and as to set the repetition frequency of the pulses in the laser beam with which to irradiate the chamfer part to a value higher than the repetition frequency in the pulses of the laser beam with which to irradiate the flat surface part.