Transient liquid-phase bonding of magnesium alloy (AZ31B) to stainless steel (304) was performed using a copper interlayer. The microstructure and bonding strength of the bonded joint were studied. The results show that when the welding condition is 510℃×30min or 530℃×10min, no eutectic phase was observed in the welded joint and the metallurgical bond is weak. When the welding condition is 520℃×30min or 530℃×20min, the joint interface produces Mg-Cu eutectic. A significant increasing occurs in weld width and interfacial bonding strength increases too. At 530℃×30min, the magnesium matrix dissolves into the eutectic liquid , and the laminar diffusion region with a width of about 350μm forms in the welded joint at the magnesium side, besides,the interface forms a metallurgical bond relying on the Mg-Cu eutectic liquid wetting and spreading to the stainless steel surface. Microstructure followed by Mg-Cu eutectic layer, Mg-rich solid solution layer , Mg17(Cu,Al)12 dispersed in magnesium alloy matrix and permeability zones of Mg-Cu-Al ternary compounds distributed in grain boundaries of magnesium alloy. The shear strength of the joint reaches the highest value of (52MPa). With the welding condition of 540℃×30min or 530℃×40min, eutectic liquid on interfacial diffusion zone occurs isothermal solidification and the joint shear strength decreases, which attributed to continuous network distributed of Mg-Cu-Al compound along the magnesium grain boundary. Recrystallization and grain growth happens to AZ31B matrix, and twins produced at 530℃×30min. The second phase precipitates within the grains and significantly grows at 540℃×30min. AZ31B matrix appears different degrees of softening phenomenon.