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. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.