A search for a high-mass Higgs boson H is performed in the H → WW → ℓνℓν and H → WW → ℓνqq decay channels using pp collision data corresponding to an integrated luminosity of 20.3 fb−1 collected at s√=8 TeV by the ATLAS detector at the Large Hadron Collider. No evidence of a high-mass Higgs boson is found. Limits on σH × BR(H → WW) as a function of the Higgs boson mass mH are determined in three different scenarios: one in which the heavy Higgs boson has a narrow width compared to the experimental resolution, one for a width increasing with the boson mass and modeled by the complex-pole scheme following the same behavior as in the Standard Model, and one for intermediate widths. The upper range of the search is mH = 1500 GeV for the narrow-width scenario and mH = 1000 GeV for the other two scenarios. The lower edge of the search range is 200–300 GeV and depends on the analysis channel and search scenario. For each signal interpretation, individual and combined limits from the two WW decay channels are presented. At mH = 1500 GeV, the highest-mass point tested, σH × BR(H → WW) for a narrow-width Higgs boson is constrained to be less than 22 fb and 6.6 fb at 95% CL for the gluon fusion and vector-boson fusion production modes, respectively.