A measurement of the cross-section for Upsilon(1S) -> mu+mu- production in proton-proton collisions at centre of mass energy of 7 TeV is presented. The cross-section is measured as a function of the Upsilon(1S) transverse momentum in two bins of rapidity, |y(Upsilon1S)| < 1.2 and 1.2 < |y(Upsilon1S)| < 2.4. The measurement requires that both muons have transverse momentum pT(mu) > 4 GeV and pseudorapidity |eta(mu)| < 2.5 in order to reduce theoretical uncertainties on the acceptance, which depend on the poorly known polarization. The results are based on an integrated luminosity of 1.13 pb-1, collected with the ATLAS detector at the Large Hadron Collider. The cross-section measurement is compared to theoretical predictions: it agrees to within a factor of two with a prediction based on the NRQCD model including colour-singlet and colour-octet matrix elements as implemented in PYTHIA while it disagrees by up to a factor of ten with the next-to-leading order prediction based on the colour-singlet-model.