Abstract: A search for a heavy Standard Model Higgs boson decaying via H -> ZZ -> l(+)l(-)q (q) over bar, where l = e, mu, is presented. The search is performed using a data set of pp collisions at root s = 7 TeV, corresponding to an integrated luminosity of 1.04 fb(-1) collected in 2011 by the ATLAS detector at the CERN LHC collider. No significant excess of events above the estimated background is found. Upper limits at 95% confidence level on the production cross section (relative to that expected from the Standard Model) of a Higgs boson with a mass in the range between 200 and 600 GeV are derived. Within this mass range, there is at present insufficient sensitivity to exclude a Standard Model Higgs boson. For a Higgs boson with a mass of 360 GeV, where the sensitivity is maximal, the observed and expected cross section upper limits are factors of 1.7 and 2.7, respectively, larger than the Standard Model prediction.