A measurement of the cross-section for Υ (1S) → μ+μ− 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 Υ (1S) transverse momentum in two bins of rapidity, and . The measurement requires that both muons have transverse momentum and pseudorapidity in order to reduce theoretical uncertainties on the acceptance, which depend on the poorly known polarisation. 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.