We show that the typical 3-3-1 models are only self-consistent if they contain interactions that explicitly violate the lepton number. The 3-3-1 model with right-handed neutrinos can by itself work as an economical 3-3-1 model as a natural recognition of the above criteria, while it also produces an inert scalar triplet (?) responsible for dark matter. This is ensured by a Z2 symmetry (assigned so that only ?is odd while all other multiplets which perform the economical 3-3-1 model are even), which is not broken by the vacuum. The minimal 3-3-1 model can provide dark matter by a similar realization. Taking the former into account, we show that the dark matter candidate (H?) contained in ? transforms as a singlet in the effective limit under the standard model symmetry and is naturally heavy. The H? relic density and direct detection cross section will have the correct values when the mass of H? is in TeV range, as expected. The model predicts the H? mass mH?=?5ì2??TeV and the H?-nucleon scattering cross section?H?-N=1.56ì10-44??cm2, provided that the new neutral Higgs boson is much heavier than the dark matter.