A measurement of the production cross-section for top quark pairs (t (t) over bar) in pp collisions at root s = 7 TeV is presented using data recorded with the ATLAS detector at the Large Hadron Collider. Events are selected in two different topologies: single lepton (electron e or muon mu) with large missing transverse energy and at least four jets, and dilepton (ee, μμor e mu) with large missing transverse energy and at least two jets. In a data sample of 2.9 pb(-1), 37 candidate events are observed in the single-lepton topology and 9 events in the dilepton topology. The corresponding expected backgrounds from non-t (t) over bar Standard Model processes are estimated using data-driven methods and determined to be 12.2 +/- 3.9 events and 2.5 +/- 0.6 events, respectively. The kinematic properties of the selected events are consistent with SM t (t) over bar production. The inclusive top quark pair production cross-section is measured to be sigma(t (t) over bar) = 145 +/- 31 (stat.)(-27)(+42) (syst.) pb. The measurement agrees with perturbative QCD calculations.