A search is presented for a high-mass Higgs boson in the H→ZZ→ℓ+ℓ−ℓ+ℓ−H→ZZ→ℓ+ℓ−ℓ+ℓ− , H→ZZ→ℓ+ℓ−νν¯H→ZZ→ℓ+ℓ−νν¯ , H→ZZ→ℓ+ℓ−qq¯H→ZZ→ℓ+ℓ−qq¯ , and H→ZZ→νν¯qq¯H→ZZ→νν¯qq¯ decay modes using the ATLAS detector at the CERN Large Hadron Collider. The search uses proton–proton collision data at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 20.3 fb −1−1 . The results of the search are interpreted in the scenario of a heavy Higgs boson with a width that is small compared with the experimental mass resolution. The Higgs boson mass range considered extends up to 1 TeV1 TeV for all four decay modes and down to as low as 140 GeVGeV , depending on the decay mode. No significant excess of events over the Standard Model prediction is found. A simultaneous fit to the four decay modes yields upper limits on the production cross-section of a heavy Higgs boson times the branching ratio to ZZ boson pairs. 95 % confidence level upper limits range from 0.53 pb at mH=195mH=195 GeV to 0.008 pb at mH=950mH=950 GeV for the gluon-fusion production mode and from 0.31 pb at mH=195mH=195 GeV to 0.009 pb at mH=950mH=950 GeV for the vector-boson-fusion production mode. The results are also interpreted in the context of Type-I and Type-II two-Higgs-doublet models.