Recently, it was reported that a graphite-based Al-ion battery is capable of operating under extremely high charge/discharge rate. This raises an interesting problem concerning how the AlCl4 clusters can diffuse so fast in the graphite cathode. In this paper, we first demonstrate by means of density functional theory calculations that AlCl4 cluster exists in graphite with planar quadrangle geometry, rather than a tetrahedral structure. Upon AlCl4 intercalation, the interlayer spacing distance between graphene layers is substantially enlarged from 3.353Å to 6.025Å. With such a large spacing, the AlCl4 diffusion becomes very easy with migration energy barriers ranging from 0.023 to 0.089eV for different migration paths in a 2-dimensional diffusion plane. These results give underlying explanation to the dynamic performance of the graphite-based Al-ion batteries.