The normalized differential cross section for top-quark pair production in association with at least one jet is studied as a function of the inverse of the invariant mass of the t t ¯ + 1-jet system. This distribution can be used for a precise determination of the top-quark mass since gluon radiation depends on the mass of the quarks. The experimental analysis is based on proton-proton collision data collected by the ATLAS detector at the LHC with a centre-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.6 fb −1 . The selected events were identified using the lepton+jets top-quark-pair decay channel, where lepton refers to either an electron or a muon. The observed distribution is compared to a theoretical prediction at next-to-leading-order accuracy in quantum chromodynamics using the pole-mass scheme. With this method, the measured value of the top-quark pole mass, m t pole , is: m t pole = 173.7 ± 1.5 stat . ± 1.4 syst . − 0.5 + 1.0 theory GeV.