Cross sections of the 54Fe(n,p)54Mn, 54Fe(n,α)51Cr, 56Fe(n,p)56Mn and 204Pb (n,2n)203Pb reactions induced by D–T neutrons were obtained with activation method and γ-ray spectrometry technique. Experimental values measured in this work are consistent with most of the previous literature data. These reactions cross sections were theoretically calculated by using the TALYS-1.96 and EMPIRE-3.2.3 codes from threshold up to 20 MeV, and significant discrepancies were found between calculated results and experiment data. In addition, experimental values are compared with evaluated nuclear data of the CENDL-3.2, ENDF/B-VIII.0, JENDL-5, BROND-3.1 and JEFF-3.3 libraries, and significant difference was found for the 54Fe(n,α)51Cr reaction in ENDF/B-VIII.0 library but not for other reactions.