The gas metal arc welding is a complex chaotic dynamic process. To study the relationship between arc electrical signal and welding stability, the multi-scale entropy method was introduced to analyze the current signals under different welding process parameters. Under the short-circuiting droplet transition mode, the larger shielding gas flow rate led to, the more stable welding and the smaller amplitude of multi-scale entropy curves. When the welding current parameter increased gradually, the droplet transition mode changed, and the amplitude of multi-scale entropy curves increased. As the welding voltage rose, the droplet transfer frequency decreased and the multi-scale entropy increased. Furthermore, the four-class prediction of welding forming quality was studied by combining with the genetic algorithm-based support vector machine (GA-SVM). The multi-scale entropy distribution was closely related to the type and stability of short-circuiting transfer in the welding process.