A search for doubly charged scalar bosons decaying into W boson pairs is presented. It uses a data sample from proton-proton collisions corresponding to an integrated luminosity of 36.1fb-1 collected by the ATLAS detector at the LHC at a centre-of-mass energy of 13TeV in 2015 and 2016. This search is guided by a model that includes an extension of the Higgs sector through a scalar triplet, leading to a rich phenomenology that includes doubly charged scalar bosons H +/-+/-. Those bosons are produced in pairs in proton-proton collisions and decay predominantly into electroweak gauge bosons H +/-+/- W +/- W +/-. Experimental signatures with several leptons, missing transverse energy and jets are explored. No significant deviations from the Standard Model predictions are found. The parameter space of the benchmark model is excluded at 95% confidence level for H +/-+/- bosons with masses between 200 and 220 GeV.