This paper investigated the formation and the growth of intermetallic compound (IMC) layer at the interface between Sn0.7Ag0.5Cu (SAC0705) solder and Cu or graphene-coated Cu (G-Cu) substrates during soldering and aging. The samples were soldered on a heating platform by aging treatment at 120 °C for up to 600 h. The experimental results showed that the thickness of IMC increased with the increasing aging time. The Cu6Sn5 IMC layer was observed between SAC0705/Cu and SAC0705/G-Cu interfaces. As the addition of Ni element in the solder, Cu6Sn5 transform into (Cu, Ni)6Sn5. With the increase of Ni content, the thickness of IMC showed an increase trend first and then decreased on the two kinds of substrates. Moreover, as the Ni content adds, the growth rate constant of interfacial IMC layer decreased. Since the graphene layer works as a diffusion barrier, the IMC on G-Cu is thinner than that on Cu substrate. And the growth rate constant of the interfacial IMC on G-Cu substrate is lower than that on Cu substrate.