To eliminate the Bi segregation and interfacial embrittlement of the SnBi/Cu joints, we deliberately added some Ag or Zn elements into the Cu substrate. Then, the reliability of the SnBi/Cu–X (X = Ag or Zn) solder joints was evaluated by investigating their interfacial reactions, tensile property, and fatigue life compared with those of the SnBi/Cu and SnAg/Cu joints. The experimental results demonstrate that even after aging for a long time, the addition of the Ag or Zn elements into the Cu substrate can effectively eliminate the interfacial Bi embrittlement of the SnBi/Cu–X joints under tensile or fatigue loadings. Compared with the conventional SnAg/Cu joints, the SnBi/Cu–X joints exhibit higher adhesive strength and comparable fatigue resistance. Finally, the fatigue and fracture mechanisms of the SnBi/Cu–X solder joints were discussed qualitatively. The current findings may pave the new way for the Sn–Bi solder widely used in the electronic interconnection in the future.