The double-differential neutron emission cross sections for n+^56Fe reactions at incident energies of 7 -13 MeV at different angles are calculated by the UNF (abbreviation for unified, 2009 Version) code, which is based on the unified Hauser-Feshbach and exciton model. The results indicate that the higher the incident energies, the better the results, although there are some discrepancies between the calculated results and the measured data for natural iron. These discrepancies are analyzed in detail in this paper. In addition, the calculated results are also compared with the evaluated results of ENDF/B VII.0 and JEFF-3.1.1 near the angle of 90° at incident energies of 8.17 and 11.5 MeV, respectively.