Laser cut quality is strongly influenced by the cutting process parameters. In this study, 5 mm mild steel is cut with a high brightness 2.5 kW diode laser. The process parameters are optimized using systematic design of experiment (DOE) to obtain burr free laser cuts with minimal cut edge surface roughness. Varied factors include cutting speed, gas pressure, focus position, nozzle diameter and nozzle distance. The goal of this work is to relate these factors to burr formations and cut edge surface roughness. The relationship is generated and validated with help of a mathematical model, which is then used to predict and minimize burr heights and cut edge surface roughness.