Creep and electromigration (EM) have been two reliability concerns in microelectronic devices for a long time. The related failure mechanisms have been widely investigated and comprehended individually. However, there is a lack of attention with regard to the interaction(s) between current density and creep, the coupling effect of which is more analogous to the real service conditions of lead-free solder joint. In this study, a series of experiments were carried out on the simple shear lap joint to investigate the effects of current density magnitude on the creep behavior of solder joints. The results indicated that dislocation creep was the main failure mechanism for low current density sample. For high current density sample, the failure mechanism was mainly dominated by copper atom migrating process which led the joint experience a higher risk of brittle fracture failure.