Magnesium alloy AZ31B and pure copper T2 were lapped and joined by cold metal transfer (CMT) welding–brazing method by AZ61A magnesium alloy wire with a 1·2 mm diameter. Results indicated that a satisfied Mg/Cu CMT welding–brazing joint was obtained in the stable welding processes with no spatter. The joint was composed of Mg–Mg welding joint formed between the Mg weld metal and the Mg base metal, and Mg–Cu brazing joint formed between the Mg weld metal and the local molten Cu base metal. The microstructure and the intermetallic compound (IMC) distribution were inspected and analysed in detail. The interfacial reaction layers of the brazing joint consisted of Mg2Cu, Al6Cu4Mg5, MgCu2 and Mg17Al12 IMCs. The tensile shear strength of the Mg/Cu CMT welding–brazing joint could reach 172·5 N mm−1. In addition, two different fracture modes were observed: at the fusion zone and at the brazing interface.