A search for the pair production of heavy leptons (N-0, L-+/-) predicted by the type-III seesaw theory formulated to explain the origin of small neutrino masses is presented. The decay channels N-0 -> W(+/-)l(+/-) (l = e, mu, tau) and L-+/- -> W(+/-)v (v = v(e), v(mu), v(tau)) are considered. The analysis is performed using the final state that contains two leptons (electrons or muons), two jets from a hadronically decaying W boson and large missing transverse momentum. The data used in the measurement correspond to an integrated luminosity of 20.3 fb(-1) of pp collisions at root s = 8 TeV collected by the ATLAS detector at the LHC. No evidence of heavy lepton pair production is observed. Heavy leptons with masses below 325-540 GeV are excluded at the 95% confidence level, depending on the theoretical scenario considered.