Abstract: This paper is based on the establisment of the mathematics model for saddle type welding groove with the edge,given the geometric definition of the edge curves,the influence of the different cutting tracks to the principle error Δb of the height of the edge was discussed.The length change Δm of groove generatrix has an effect on the distance a between cutting torch and workpiece,the eliminate method that the existence of Δm which causes the distance between cutting torch and workpiece changes Δa is introduced.The establisment of the mathematical model for saddle type welding groove with the edge,by the welding groove geometric model to calculate the Δm and set the method of Δm and cutting intersection angle θ curves is descriked.It concluse that using the edge curves as the cutting tracks can eliminate the change of Δa caused by the Δm and improve the cutting quality and accuracy.