A search for a new massive charged gauge boson, W′, is performed with the ATLAS detector at the LHC. The dataset used in this analysis was collected from proton-proton collisions at a centre-of-mass energy of s = 13 TeV, and corresponds to an integrated luminosity of 139 fb−1. The reconstructed tb invariant mass is used to search for a W′ boson decaying into a top quark and a bottom quark. The result is interpreted in terms of a W′ boson with purely right-handed or left-handed chirality in a mass range of 0.5–6 TeV. Different values for the coupling of the W′ boson to the top and bottom quarks are considered, taking into account interference with single-top-quark production in the s-channel. No significant deviation from the background prediction is observed. The results are expressed as upper limits on the W′ → tb production cross-section times branching ratio as a function of the W′-boson mass and in the plane of the coupling vs the W′-boson mass.