A search is reported for a neutral Higgs boson in the decay channel H->Z gamma, Z->l+l- (l=e, mu), using 4.5 fb-1 of pp collisions at sqrt(s) = 7 TeV and 20.3 fb-1 of pp collisions at sqrt(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, m(llgamma), 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 sqrt(s)=8 TeV at 95% confidence level.