A measurement of the mass of the W boson is presented based on proton-proton collision data recorded in 2011 at a centre-of-mass energy of 7 TeV with the ATLAS detector at the LHC, and corresponding to 4.6 fb(-1) of integrated luminosity. The selected data sample consists of 7.8 x 10(6) candidates in the W -> mu nu channel and 5.9 x 10(6) candidates in the W -> e nu channel. The W-boson mass is obtained from template fits to the reconstructed distributions of the charged lepton transverse momentum and of the W boson transverse mass in the electron and muon decay channels, yielding

m(W) = 80370 +/- 7 (stat.) +/- 11(exp. syst.)

+/- 14 (mod. syst.) MeV

= 80370 +/- 19 MeV,

where the first uncertainty is statistical, the second corresponds to the experimental systematic uncertainty, and the third to the physics-modelling systematic uncertainty. A measurement of the mass difference between the W+ and W- bosons yields m(W+) - m(W-) = -29 +/- 28 MeV.