  We extend the scalar sector of the neutrinophilic two Higgs doublet model,
where small masses of Dirac neutrinos are obtained via a small vacuum
expectation value v_nu of the neutrinophilic SU(2)_L-doublet scalar field which
has a Yukawa interaction with only right-handed neutrinos. A global U(1)_X
symmetry is used for the neutrinophilic nature of the second SU(2)_L-doublet
scalar field and also for eliminating Majorana mass terms of neutrinos. By
virtue of an appropriate assignment of the U(1)_X-charges to new particles, our
model has an unbroken Z_2 symmetry, under which the lightest Z_2-odd scalar
boson can be a dark matter candidate. In our model, v_nu is generated by the
one-loop diagram to which Z_2-odd particles contribute. We briefly discuss a
possible signature of our model at the LHC.
