•The degree mismatch between Al (111) and Al4C3 (0001) interface was the lowest.•Al-C covalent bonds and Al-Al metallic bonds increased interfacial bonding strength.•α-Al nucleus tend to form on the C-termination-center-sited Al4C3 (0 0 0 1). The graphene (Gr) reacted with Al, and the Al4C3 phase was precipitated during selective laser melting (SLM). The interfacial structure of Al/Al4C3 was calculated by the first principle. The degree mismatch between Al (1 1 1) and Al4C3 (0 0 0 1) interface was lowest. Al (1 1 1)/Al4C3 (0 0 0 1) interface models with different stacking sequences (top-site, center-site, and hollow-site) of different terminations (Al-termination and C-termination) were established. C-termination-center-sited interface has largest work of adhesion, and interfacial energy of this model is lower than that of α-Al/Al melt (0.15 J/m2), so that α-Al nucleus tend to form on the C-termination-center-sited Al4C3 (0 0 0 1). Al-C covalent bonds and Al-Al metallic bonds are formed across interface, which increased interfacial bonding strength.