In this paper, finite element calculations are used to simulate the melting flow pattern within a titanium/steel dissimilar welded joint with Cu as the transition layer under an oscillating laser welding process, and these calculations are used as a guide for bias oscillating laser welding experiments. When using 304SS side bias oscillating laser welding, welded joints with a tensile strength of 395 MPa were obtained. Compared to the linear bias welding process, it was found that the bias oscillation laser welding process can, on the one hand, generate a stirring effect on the melting pool during the welding process, forming Fe-rich structures encapsulated by Cu layers, which in turn strengthen the Cu layers, and on the other hand, effectively reduce the content of Fe-Ti brittle intermetallic compounds in the weld and obtain a Cu-Ti IMC layer with a thickness of only 10 μm, thus significantly improving the tensile strength of the weld joint and reducing the possibility of incidental fracture.