Density functional calculations have been thoroughly employed to investigate the electronic structures of gold clusters on hematite surface. Obtained results indicate that in practical types of terminations the Fe-O3-Fe surface has unique capability of supporting gold clusters to be thermodynamically stable with the binding energies of 2.82, 2.25 and 3.53 eV for Au, Au2 and Au3 respectively. In detail, gold atoms in gold clusters are found to be locating at the position on the top of iron of the support surface and interacting with nearby oxygen atoms as well. The local density of states study reveals that overlap of the orbitals of gold and the surface's atoms is the decisive factor of the interaction between gold clusters and the substrate. This result is in a good agreement with experimental data that gold is not completely metallic when supported on hematite.