A combination of searches for a new resonance decaying into a Higgs boson pair is presented, using up to Formula Presented of Formula Presented collision data at Formula Presented recorded with the ATLAS detector at the LHC. The combination includes searches performed in three decay channels: Formula Presented, Formula Presented, and Formula Presented. No excess above the expected Standard Model background is observed and upper limits are set at the 95% confidence level on the production cross section of Higgs boson pairs originating from the decay of a narrow scalar resonance with mass in the range 251 GeV-5 TeV. The observed (expected) limits are in the range 0.96-600 fb (1.2-390 fb). The limits are interpreted in the type-I two-Higgs-doublet model and the minimal supersymmetric standard model, and constrain parameter space not previously excluded by other searches.