The development of advanced electronic devices leads to highly miniaturized interconnect circuits (ICs), which significantly increases the electromigration (EM) phenomenon of solder and circuits due to higher current density. The electromigration of solder joints under high current density has become a severe reliability concern in terms of microelectronic product reliability. The microstructure of the solder plays an important role in the electromigration induced degradation. In this study, Sn-3.0Ag-0.5Cu solder bumps with Ni/Au under bump metallization (UBM) layer were fabricated and electromigration acceleration tests were conducted under current density of 1.4 × 104 A/cm2 and 120 °C to investigate the effect of grain structure and Ni/Au-UBM layer on EM-induced failure. Grain structures of solder bumps were determined by utilizing the Electron Backscatter Diffraction (EBSD) technique, and single-crystal solder, single-crystal dominated solder, and polycrystalline solder are observed in different test samples. According to the Scanning Electron Microscope (SEM) images, it is observed that the Ni/Au-UBM layer of the Cu pad can inhibit atom diffusion between solder bump and Cu pad, which reduces the consumption of Cu pad but causes a large void and crack at the interface. The EM lifetime of single crystal solder bumps is lower than that of polycrystalline solder bumps when the c-axis of single crystal solder bumps is perpendicular to the electron flow direction. Additionally, the single crystal structure will increase the brittleness of the solder bump, and cracks are easily generated and expanded under the stress caused by the mismatch of thermal expansion coefficients between the solder bump and Ni/Au-UBM layer near Cu pad. Polycrystalline solder bumps with a higher misorientation angle (15–55°) have a higher atom diffusion rate, which will result in the acceleration of the EM-induced failure.