A search for doubly charged Higgs bosons with pairs of prompt, isolated, highly energetic leptons with the same electric charge is presented. The search uses a proton-proton collision data sample at a centre-of-mass energy of 13 TeV corresponding to 36.1 fb(-1) of integrated luminosity recorded in 2015 and 2016 by the ATLAS detector at the LHC. This analysis focuses on the decays H-+/-+/- -> e(+/-)e(+/-), H-+/-+/- -> e(+/-)mu(+/-) and H-+/-+/- -> mu(+/-)mu(+/-), fitting the dilepton mass spectra in several exclusive signal regions. No significant evidence of a signal is observed and corresponding limits on the production cross-section and consequently a lower limit on m(H-+/-+/-) are derived at 95% confidence level. With l(+/-)l(+/-) = e(+/-)e(+/-)/mu(+/-)mu(+/-)/e(+/-)mu(+/-), the observed lower limit on the mass of a doubly charged Higgs boson only coupling to left-handed leptons varies from 770 to 870GeV (850GeV expected) for B(H-+/-+/- -> l(+/-)l(+/-)) = 100% and both the expected and observed mass limits are above 450GeV for B(H-+/-+/- -> l(+/-)l(+/-)) = 10% and any combination of partial branching ratios.