The results of a search for new heavy W' bosons decaying to an electron or muon and a neutrino using proton-proton collision data at a centre-of-mass energy of root s = 13 TeV are presented. The dataset was collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider and corresponds to an integrated luminosity of 36.1 fb(-1). As no excess of events above the Standard Model prediction is observed, the results are used to set upper limits on the W' boson cross-section times branching ratio to an electron or muon and a neutrino as a function of the W' mass. Assuming a W' boson with the same couplings as the Standard Model W boson, W' masses below 5.1 TeV are excluded at the 95% confidence level.