Abstract: The welding process of complex space curve, such as intersection seam of sphere and tube, is difficult in the field of welding automation, and the construction of a mathematical model of intersection seam is a prerequisite for the welding process. After a mathematical model of intersection curve of sphere and tube is established with MATLAB software, by further analysis, the intersection curve can be simplified to plane curve. By considering the thickness effects of the sphere, some amendments to the model of J-shaped groove weld are made by increasing △D and △d two corrections in the diameter directions of sphere and tube respectively. All functions such as graphics and output data, are integrated into a GUI(Graphics User Interface) based on MATLAB programming, and the GUI is converted to a standalone application which is efficient and convenient, which provided a theoretical basis for robot welding and controlling of this seam weld.