This Letter presents direct searches for lepton flavour violation in Higgs boson decays, H→eτ and H→μτ, performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton–proton collisions at a centre-of-mass energy s=13 TeV, corresponding to an integrated luminosity of 36.1 fb−1. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95% confidence-level upper limits on the lepton-flavour-violating branching ratios are 0.47% (0.34−0.10+0.13%) and 0.28% (0.37−0.10+0.14%) for H→eτ and H→μτ, respectively.