Abstract: The surface structures of Fe₃O₄(111), (110) and (001) have been studied at the level of density functional theory. It is found that there are two most stable Fe3O4(111) surfaces in close energy and terminated with the exposed tetrahedral and octahedral iron layers. Both Fe₃O₄(110) and Fe₃O₄(001) surfaces have two surface terminations in close energy. The computed results agree well with the experiments, and explain reasonably the observed diversity and complexity of the experiments. The computed surface free energies indicate that (111) is less favourable thermodynamically than (110) and (001), and the formation of (111) should be kinetic controlled.