An energy beam method and apparatus for processing a workpiece is accomplished by making the energy density per unit time and unit area of the energy beam proportional to the traveling velocity of the workpiece. This is accomplished by adjusting the frequency, irradiation power, or duty cycle of the energy beam. The travel velocity of the workpiece is measured by using a linear scale to generate pulse signals, calculating a traveling velocity based on the pulse signals and generating a pulse signal, dividing the pulse signals output by the calculation step, and generating a trigger signal in response to the pulse signals created by the dividing step to drive an energy beam irradiation device (such as a laser generator) to output the energy beam.