A search for the Standard Model Higgs boson produced in association with a top-quark pair, tt¯H , is presented. The analysis uses 20.3 fb −1 of pp collision data at s=8TeV , collected with the ATLAS detector at the Large Hadron Collider during 2012. The search is designed for the H→bb¯ decay mode and uses events containing one or two electrons or muons. In order to improve the sensitivity of the search, events are categorised according to their jet and b -tagged jet multiplicities. A neural network is used to discriminate between signal and background events, the latter being dominated by tt¯ +jets production. In the single-lepton channel, variables calculated using a matrix element method are included as inputs to the neural network to improve discrimination of the irreducible tt¯+bb¯ background. No significant excess of events above the background expectation is found and an observed (expected) limit of 3.4 (2.2) times the Standard Model cross section is obtained at 95 % confidence level. The ratio of the measured tt¯H signal cross section to the Standard Model expectation is found to be μ=1.5±1.1 assuming a Higgs boson mass of 125 GeV .