Occupancy sites of uranium atom in goethite are studied by first principles calculations. It is found that the formation energies of substitution (S), octahedral (O), and tetrahedral (T) sites of uranium in goethite are -13.49, -3.86, and -1.60 eV, respectively. The formation energies of dual uranium in S and O sites in goethite are -27.392 and -16.214 eV, respectively, and corresponding binding energies are -0.417 and 1.131 eV, respectively. It is concluded that dual uranium atoms can aggregate together in S site formation in goethite, but not in O site formation.