The production cross-section of a top quark in association with a W boson is measured using proton–proton collisions at s=8TeV. The dataset corresponds to an integrated luminosity of 20.2fb-1, and was collected in 2012 by the ATLAS detector at the Large Hadron Collider at CERN. The analysis is performed in the single-lepton channel. Events are selected by requiring one isolated lepton (electron or muon) and at least three jets. A neural network is trained to separate the tW signal from the dominant tt¯ background. The cross-section is extracted from a binned profile maximum-likelihood fit to a two-dimensional discriminant built from the neural-network output and the invariant mass of the hadronically decaying W boson. The measured cross-section is σtW=26±7pb, in good agreement with the Standard Model expectation.