Abstract: A search for the production of single top-quarks via flavour-changing neutral-currents is presented. Data collected with the ATLAS detector at a centre-of-mass energy of root s = 7 TeV, corresponding to an integrated luminosity of 2.05 fb(-1), are used. Candidate events with a semileptonic top-quark decay signature are classified as signal- or background-like events by using several kinematic variables as input to a neural network. No signal is observed in the neural network output distribution and a Bayesian upper limit is placed on the production cross-section. The observed upper limit at 95% confidence level 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 is converted using a model-independent approach into upper limits on the coupling strengths kappa(ugt)/Lambda < 6.9.10(-3) TeV-1 and kappa(cgt)/Lambda < 1.6.10(-2) TeV-1, where A is the new physics scale, and on the branching fractions B(t -> ug) < 5.7.10(-5) and B(t -> cg) < 2.7.10(-4).