This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb−1 of proton–proton collision data at a centre-of-mass energy s=13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the bb¯bb¯, bb¯W+W−, bb¯τ+τ−, W+W−W+W−, bb¯γγ and W+W−γγ final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio (κλ) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to −5.0<12.0 (−5.8<12.0). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza–Klein Randall–Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model.