A search for a Standard Model Higgs boson decaying via H→ZZ→ℓ+ℓ−νν¯, where ℓ represents electrons or muons, is presented. It is based on proton–proton collision data at s=7TeV, collected by the ATLAS experiment at the LHC during 2011 and corresponding to an integrated luminosity of 4.7fb−1. The data agree with the expected Standard Model backgrounds. Upper limits on the Higgs boson production cross section are derived for Higgs boson masses between 200 GeV and 600 GeV and the production of a Standard Model Higgs boson with a mass in the range 319–558 GeV is excluded at the 95% confidence level.