Proton–proton collision data recorded by the ATLAS detector in 2011, at a centre-of-mass energy of 7 TeV, have been used for an improved determination of the W-boson mass and a first measurement of the W-boson width at the LHC. Recent fits to the proton parton distribution functions are incorporated in the measurement procedure and an improved statistical method is used to increase the measurement precision. The measurement of the W-boson mass yields a value of $m_W = 80{,}366.5 \pm 9.8~(\text {stat.}) \pm 12.5~(\text {syst.})$ MeV $= 80{,}366.5 \pm 15.9$ MeV, and the width is measured as $\Gamma _W = 2202 \pm 32~(\text {stat.}) \pm 34~(\text {syst.})$ MeV $= 2202 \pm 47$ MeV. The first uncertainty components are statistical and the second correspond to the experimental and physics-modelling systematic uncertainties. Both results are consistent with the expectation from fits to electroweak precision data. The present measurement of $m_W$ is compatible with and supersedes the previous measurement performed using the same data.