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, |yϒ(1S)|<1.2 and 1.2<|yϒ(1S)|<2.4. The measurement requires that both muons have transverse momentum pTμ>4 GeV and pseudorapidity |ημ|<2.5 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.