The reliabilities of solder joints, which are closely related to the microstructure and mechanical properties of solder joints, are important for electronic packaging. In this work, the growth behaviors of microstructure in Sn3.0Ag0.5Cu/Cu solder joints, including intermetallic compounds and Sn dendrites, were investigated when different cooling methods—quenched in water, cooling in air, and cooling in a furnace after reflow—were used. Local enrichment of element was observed with the quadrant backscattering diffraction and energy dispersive spectrometer in the sample quenched in water. The growth mechanism of microstructure in Sn3.0Ag0.5Cu/Cu solder joint was discussed. The results of tensile tests indicated that the enrichment of element induced a hardening effect. Moreover, plate-like Ag3Sn compounds and oversize Sn dendrites were apt to reduce the tensile strength of solder joint.