  Although the seesaw mechanism is a natural explanation for the small neutrino
masses, there are cases when the Majorana mass terms for the right-handed
neutrinos are not allowed due to symmetry. In that case, if neutrino-specific
Higgs doublet is introduced, neutrinos become Dirac particles and their small
masses can be explained by its small VEV. We show that the same symmetry, which
we assume a global $U(1)_X$, can also be used to explain the stability of dark
matter. In our model, a new singlet scalar breaks the global symmetry
spontaneously down to a discrete $Z_2$ symmetry. The dark matter particle,
lightest $Z_2$-odd fermion, is stabilized. We discuss the phenomenology of dark
matter: relic density, direct detection, and indirect detection. We find that
the relic density can be explained by a novel Goldstone boson channel or by
resonance channel. In the most region of parameter space considered, the direct
detections is suppressed well below the current experimental bound. Our model
can be further tested in indirect detection experiments such as FermiLAT gamma
ray searches or neutrinoless double beta decay experiments.
