Results on the search for flavor-changing neutral-current single top-quark production are reported. Data collected with the ATLAS detector at a center-of-mass energy of sqrt(s) = 7 TeV and corresponding to an integrated luminosity of 2.05 fb^-1 are used. Candidate events with a leptonic top-quark decay signature are classified into signal- and background-like events using a neural network. No signal is observed in the output distribution and a Bayesian upper limit on the production cross-section is placed. The observed 95% C.L. upper limit on the cross-section multiplied by the t -> Wb branching fraction is measured to be sigma(qg -> t) x B(t -> Wb) < 3.9 pb. This upper limit can be converted into an upper limit of the coupling strength k_ugt/Lambda < 6.9 x 10^-3 TeV^-1 and k_cgt/Lambda < 1.6 x 10^-2 TeV^-1 and on the branching fractions B(t -> ug) < 5.7 x 10^-5 and B(t -> cg) < 2.7 x 10^-4.