  We propose a simple non-supersymmetric lepton flavor model with $A_4$
symmetry. The $A_4$ group is a minimal one which includes triplet irreducible
representation. We introduce three Higgs doublets which are assigned as triplet
of the $A_4$ symmetry. It is natural that there are three generations of the
Higgs fields as same as the standard model fermions. We study the potential
analysis and we get the vacuum expectation values for the local minimum. In the
vacuum expectation values, we obtain the charged lepton, Dirac neutrino, and
right-handed Majorana neutrino mass matrices. By using type-I seesaw mechanism,
we get the left-handed Majorana neutrino mass matrix. In the NuFIT 5.1 data, we
predict the Dirac CP phase and the Majorana phases for the only inverted
neutrino mass hierarchy. Especially, the Dirac CP phase and lepton mixing angle
$\theta_{23}$ are strongly correlated. If the $\theta_{23}$ is more precise
measured, the Dirac CP phase is more precise predicted, and vice versa. We also
predict the effective mass for neutrino-less double beta decay $m_{ee}\simeq
47.1~[\mathrm{meV}]$ and the lightest neutrino mass $m_3\simeq
0.789$~-~$1.43~[\mathrm{meV}]$. It is testable for our model in the near future
neutrino experiments.
