Aiming at the problem of high apex angle burnt rate during laser cutting graphics with apex angle (≤30°) on mild or low carbon steel, the laser cutting experiments have been done on A3 steel board with the thickness of 3 mm by using Rofin DC025 slab CO2 laser cutting system and the method of path transformation. At the same time, the key effects of temperature on apex angle burnt have been analyzed, and the influences of path transformation and its radius on apex angle burnt rate have been studied. The results show that the apex angle burnt rate has been greatly reduced under the condition of a special cutting path, which is a circle passing through the zenith of the apex angle and its centre locating on angle bisector. Meanwhile, the apex angle burnt rate can be controlled lower than 10% under the condition of a optimal circle radius for various apex angle.