Abstract: A direct search for lepton-flavour-violating H -> μtau decays of the recently discovered Higgs boson with the ATLAS detector at the LHC is presented. The analysis is performed in the H -> μtau(had) channel, where tau(had) is a hadronically decaying tau-lepton. The search is based on the data sample of proton-proton collisions collected by the ATLAS experiment corresponding to an integrated luminosity of 20.3 fb(-1) at a centre-of-mass energy of root s = 8TeV. No statistically significant excess of data over the predicted background is observed. The observed (expected) 95% confidence-level upper limit on the branching fraction, Br(H -> μtau), is 1.85% (1.24%).