A search for new charged massive gauge bosons, W′, is performed with the ATLAS detector at the LHC. Data were collected in proton–proton collisions at a center-of-mass energy of s=13 TeV and correspond to an integrated luminosity of 36.1 fb−1. This analysis searches for W′ bosons in the W′→tb¯ decay channel in final states with an electron or muon plus jets. The search covers resonance masses between 0.5 and 5.0 TeV and considers right-handed W′ bosons. No significant deviation from the Standard Model (SM) expectation is observed and upper limits are set on the W′→tb¯ cross section times branching ratio and the W′ boson effective couplings as a function of the W′ boson mass. For right-handed W′ bosons with coupling to the SM particles equal to the SM weak coupling constant, masses below 3.15 TeV are excluded at the 95% confidence level. This search is also combined with a previously published ATLAS result for W′→tb¯ in the fully hadronic final state. Using the combined searches, right-handed W′ bosons with masses below 3.25 TeV are excluded at the 95% confidence level.