A search for the Standard Model Higgs boson produced in association with a top-quark pair, $t\bar{t}H$, is presented. The analysis uses 36.1 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}$ = 13 TeV, collected with the ATLAS detector at the Large Hadron Collider in 2015 and 2016. The search targets the $H \to b\bar{b}$ decay mode. Events are selected to contain either one or two electrons or muons from the top-quark decays, and are then categorised according to the number of jets and how likely these are to contain $b$-hadrons. Multivariate techniques are used to discriminate between signal and background events, the latter being dominated by $t\bar{t}$ + jets production. For a Higgs boson mass of 125 GeV, the ratio of the measured $t\bar{t}H$ signal cross-section to the Standard Model expectation is found to be $\mu = 0.84^{+0.64}_{-0.61}$. A value of $\mu$ higher than 2.0 is excluded at the 95% confidence level, the expected exclusion limit in the absence of signal being 1.2.

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