Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via H ± → τ ± ν τ , are searched for in 36.1 fb −1 of proton-proton collision data at √s = 13 TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with H ± decays hadronically or leptonically, the search targets τ +jets and τ +lepton final states, in both cases with a hadronically decaying τ -lepton. No evidence of a charged Higgs boson is found. For the mass range of m H ± = 90–2000 GeV, upper limits at the 95% confidence level are set on the production cross-section of the charged Higgs boson times the branching fraction ℬ H ± → τ ± ν τ in the range 4.2–0.0025 pb. In the mass range 90–160 GeV, assuming the Standard Model cross-section for t t ¯ production, this corresponds to upper limits between 0.25% and 0.031% for the branching fraction ℬ t → b H ± × ℬ H ± → τ ± ν τ .