To solve the challenge of welding aluminum alloys, a unified adjustment model for Gaussian pulse welding is established. This model can achieve improved welding performance by adjusting the base current of the weak pulse group within a specific range of average welding current inputs. The flat overlaying welding is carried out on the base material: 6061 aluminum alloys with thicknesses of 2 mm, 3 mm, and 5 mm. A stable welding process, indicated by reduced spatter, is produced, with a soft arc sound and good repeatability in the waveforms of the real-time current and voltage. The weld has a shiny surface and regular fish scale ripples. Metallographic analysis shows that the fusion line is clear, and there are no visible defects, while the weld zone has fine dendritic structures. The tensile test results indicate that fractures occur in the heat-affected zone, and that the tensile strength reaches about 68% of that of the base metal.