A search for the Standard Model Higgs boson decaying into a pair of tau leptons is reported. The analysis is based on a data sample of proton-proton collisions collected by the ATLAS experiment at the LHC and corresponding to an integrated luminosity of 4.7 fb(-1). No significant excess over the expected background is observed in the Higgs boson mass range of 100-150GeV. The observed (expected) upper limits on the cross section times the branching ratio for H -> tau(+)tau(-) are found to be between 2.9 (3.4) and 11.7 (8.2) times the Standard Model prediction for this mass range.