A measurement of the cross-section for gamma(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 gamma(1S) transverse momentum in two bins of rapidity, vertical bar y(gamma(1S))vertical bar < 1.2 and 1.2 < vertical bar y(gamma(1S))vertical bar < 2.4. The measurement requires that both muons have transverse momentum p(T)(mu) > 4 GeV and pseuclorapidity vertical bar eta(mu)vertical bar < 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. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.