As observed in a number of experiments in literature,[1-5] the aluminum carbide (Al4C3) has a morphology of a needle-like structure at the graphite-aluminum interface. Owing to the influence of this needle-like structure, it is well known that the aluminum carbide crystal is brittle. In addition, the aluminum carbide is recognized as highly sensitive to moisture contact. Thus, a degeneration of the mechanical properties of the composite is observed and the formation of Al4C3 should be avoided.[6-7] In the present work, we use a phase-field model based on a grand potential formulation incorporating the Gibbs free energies of the individual phases from thermodynamical data bases to investigate the growth of the aluminum carbide at the graphite-aluminum interface. The equilibrium shape of the needle-like structure in principle can be determined by the Wulff construction by constructing an elliptic anisotropy for the interfacial energy. As reported in literature, when the strength of the interfacial energy anisotropy is too large, e.g. greater than 2, "ears" appear at the edge of the Wulff shape, which is inconsistent with experimental observations. To model such a needle-like structure, we presently employ the interfacial energy anisotropy with strength less than 2, in combination with a modified kinetic anisotropy. Furthermore, we consider a scenario where a number of carbon particles are placed in the Al-liquid solution and study the growth of the aluminum carbide at the surface of the carbon particles. The effect of the size of the carbon particles and the distance between the particles are explored.