A search for new charged massive gauge bosons, called W′ , is performed with the ATLAS detector at the LHC, in proton–proton collisions at a centre-of-mass energy of s=8 TeV , using a dataset corresponding to an integrated luminosity of 20.3 fb−1 . This analysis searches for W′ bosons in the W′→tb¯ decay channel in final states with electrons or muons, using a multivariate method based on boosted decision trees. The search covers masses between 0.5 and 3.0 TeV, for right-handed or left-handed W′ bosons. No significant deviation from the Standard Model expectation is observed and limits are set on the W′→tb¯ cross-section times branching ratio and on the W′ -boson effective couplings as a function of the W′ -boson mass using the CLs procedure. For a left-handed (right-handed) W′ boson, masses below 1.70 (1.92) TeV are excluded at 95% confidence level.