Cutting by a high speed laser cutting machine is one of most effective technologies to improve productivity. This paper has studied to obtain the cutting characteristics and optimal cutting conditions in a high speed feeding type laser cutting machine by Tacuchi method in design of experiments. A Lf(34) orthogonal array is adopted to study the effect of adjustment parameter. The adjustment parameters consist of cutting speed, laser power, laser output duty and assistant gas pressure. And the quality feature is selected as surface roughness of sheet metal. Variance analysis is performed in order to evaluate the effect of adjustment parameters on the quality feature of laser cutting process.