This article presents the sensitivity of theATLAS experiment to the lepton-flavour-violating decays of τ → 3μ. A method utilising the production of τ leptons via W → τν decays is used. This method is applied to the sample of 20.3 fb-1 of pp collision data at a centre-of-mass energy of 8 TeV collected by the ATLAS experiment at the LHC in 2012. No event is observed passing the selection criteria,and the observed (expected) upper limit on the τ lepton branching fraction into three muons, Br(τ → 3μ), is 3.76 × 10-7 (3.94 × 10-7) at 90 % confidence level.