This Letter reports a measurement of the high-mass Drell–Yan differential cross-section in proton–proton collisions at a centre-of-mass energy of 7 TeV at the LHC. Based on an integrated luminosity of 4.9 fb−14.9 fb−1, the differential cross-section in the Z/γ*→e+e−Z/γ*→e+e− channel is measured with the ATLAS detector as a function of the invariant mass, meemee, in the range 116<1500 GeV116<1500 GeV, for a fiducial region in which both the electron and the positron have transverse momentum pT>25 GeVpT>25 GeV and pseudorapidity |η|<2.5|η|<2.5. A comparison is made to various event generators and to the predictions of perturbative QCD calculations at next-to-next-to-leading order.