Joining dissimilar Mg/Cu alloys was still an intractable problem because of the excessive intermetallic compounds (IMCs) and poor mechanical properties using conventional welding methods. In the present study, friction stir welding was employed for the butt joining of dissimilar AZ31B Mg-alloy and T2 pure Cu plates. Defect-free Mg/Cu joints were obtained with Mg-RS and Cu-AS configuration, at a welding speed of 50 mm/min and tool rotating speeds of 325 r/min, 625 r/min and 925 r/min. At the joining interface, both Mg2Cu and MgCu2 IMC phases were observed, with a clear, uniform and continuous IMCs layer composed of two sub-layers, layer-A of Mg+Mg2Cu and layer-B of Mg2Cu+MgCu2. The maximum ultimate tensile strength of the Mg/Cu friction stir welding joint reached 130 MPa at 925 r/min due to enhanced mechanical interlocking between Mg and Cu, as well as sufficient metallurgical bonding at the joining interface with an IMCs layer thickness in the range of 1.0-2.0 μm.