Cutting by a high speed laser cutting machine is one of most effective technologies to improve productivity. This paper has presented the cutting characteristics and optimal cutting conditions in a high speed feeding type laser cutting machine by using Tacuchi method in the design of experiment. An L9(34) orthogonal array is adopted to study the effect of adjustment parameters. The adjustment parameters consist of cutting speed, laser power, laser output duty and assistant gas pressure. The surface roughness of sheet metal is regarded as a quality feature. Analysis of variance is performed in order to evaluate the effect of adjustment parameters on the quality feature of laser cutting process.