A search is reported for a neutral Higgs boson in the decay channel H → Zγ, Z → ℓ+ℓ− (ℓ = e,μ), using 4.5 fb −1 of pp collisions at √s = 7 TeV and 20.3 fb −1 of pp collisions at √s = 8 TeV, recorded by the ATLAS detector at the CERN Large Hadron Collider. The observed distribution of the invariant mass of the three final-state particles, mℓℓγ, is consistent with the Standard Model hypothesis in the investigated mass range of 120–150 GeV. For a Higgs boson with a mass of 125.5 GeV, the observed upper limit at the 95% confidence level is 11 times the Standard Model expectation. Upper limits are set on the cross section times branching ratio of a neutral Higgs boson with mass in the range 120–150 GeV between 0.13 and 0.5 pb for √s = 8 TeV at 95% confidence level.