In this paper, arcs on the 0.5 mm pure thick aluminum (1060) sheet is cut precisely by Nd:YAG pulse laser, to eliminate roughness differences of laser cutting stencil, the microstructure of kerf results is obtained through microscope, which provides the basis to set up the simplified mathematical model. Formulas to estimate the kerf surface roughnesses of these arcs are presented, and the effect laws of radius size on the kerf surface roughnesses differences with the same cutting parameters are analyzed particularly. The results show that, with decreasing the radii of outside arc and inside arc, the kerf roughnesses are improved; when the radius R≤7 mm, the roughnesses of these two arcs are different significantly; when the radius R>7 mm, the differences of these roughnesses almost disappear. At last, optimizing the kerf roughnesses of all shapes by response surface method (RSM) minimize optimization and target optimization respectively to obtain the cutting parameters, the roughnesses of all shapes cut by above cutting parameters are almost same, therefore this method eliminates the linear and circular roughness differences, which is feasible and effective.