  We construct a $D_4$ flavor model based on SU(3)_C X SU}(3_L X U(1)_X gauge
symmetry responsible for fermion masses and mixings. The neutrinos get small
masses from antisextets which are in a singlet and a doublet under $D_4$. If
the D_4 symmetry is violated as perturbation by a Higgs triplet under SU(3)_L
and lying in {1}''' of D_4, the corresponding neutrino mass mixing matrix gets
the most general form. In this case, the model can fit the experimental data in
2012 on neutrino masses and mixing. Our results show that the neutrino masses
are naturally small and a little deviation from the tribimaximal neutrino
mixing form can be realized. The quark masses and mixing matrix are also
discussed. In the model under consideration, the CKM matrix can be different
from the unit matrix. The scalar potential of the model is more simpler than
those of the model based on $S_3$ and $S_4$. Assignation of VEVs to antisextets
leads to the mixing of the new gauge bosons and those in the Standard Model.
The mixing in the charged gauge bosons as well as the neutral gauge boson is
considered.
