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) over bar + 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 7TeV 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) t = 173.7 +/- 1.5 (stat.) +/- 1.4 (syst.)(-0.5)(+1.0) (theory) GeV. This result represents the most precise measurement of the top-quark pole mass to date.