Narrow resonances decaying into WW, WZ or ZZ boson pairs are searched for in 36.7 fb−1 of proton–proton collision data at a centre-of-mass energy of √s=13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015 and 2016. The diboson system is reconstructed using pairs of large-radius jets with high transverse momentum and tagged as compatible with the hadronic decay of high-momentum W or Z bosons, using jet mass and substructure properties. The search is sensitive to diboson resonances with masses in the range 1.2–5.0 TeV. No significant excess is observed in any signal region. Exclusion limits are set at the 95% confidence level on the production cross section times branching ratio to dibosons for a range of theories beyond the Standard Model. Model-dependent lower limits on the mass of new gauge bosons are set, with the highest limit set at 3.5 TeV in the context of mass-degenerate resonances that couple predominantly to bosons.