A search is performed for narrow resonances decaying into WW, WZ, or ZZ boson pairs using 20.3 fb(-1) of proton-proton collision data at a centre-of-mass energy of root s = TeV recorded with the ATLAS detector at the Large Hadron Collider. Diboson resonances with masses in the range from 1.3 to 3.0 TeV are sought after using the invariant mass distribution of dijets where both jets are tagged as a boson jet, compatible with a highly boosted W or Z boson decaying to quarks, using jet mass and substructure properties. The largest deviation from a smoothly falling background in the observed dijet invariant mass distribution occurs around 2 TeV in the WZ channel, with a global significance of 2.5 standard deviations. Exclusion limits at the 95% confidence level are set on the production cross section times branching ratio for the WZ final state of a new heavy gauge boson, W', and for the WW and ZZ final states of Kaluza-Klein excitations of the graviton in a bulk Randall-Sundrum model, as a function of the resonance mass. W' bosons with couplings predicted by the extended gauge model in the mass range from 1.3 to 1.5 TeV are excluded at 95% confidence level.