A measurement of the top-quark mass (m_t) in the tt¯ → lepton + jets channel is presented, with an experimental technique which exploits semileptonic decays of b-hadrons produced in the top-quark decay chain. The distribution of the invariant mass m_ℓμ of the lepton, ℓ (with ℓ = e, μ), from the W-boson decay and the muon, μ, originating from the b-hadron decay is reconstructed, and a binned-template profile likelihood fit is performed to extract m_t. The measurement is based on data corresponding to an integrated luminosity of 36.1 fb⁻¹ of s = 13 TeV pp collisions provided by the Large Hadron Collider and recorded by the ATLAS detector. The measured value of the top-quark mass is m_t = 174.41 ± 0.39 (stat.) ± 0.66 (syst.) ± 0.25 (recoil) GeV, where the third uncertainty arises from changing the Pythia8 parton shower gluon-recoil scheme, used in top-quark decays, to a recently developed setup. [Figure not available: see fulltext.].