  We discuss a supersymmetric model with discrete flavor symmetry $A_4\times
Z_3$. The additional scalar fields which contribute masses of leptons in the
Yukawa terms are introduced in this model. We analyze their scalar potential
and find that they have various vacuum structures. We show the relations among
24 different vacua and classify them into two types. We derive expressions of
the lepton mixing angles, Dirac CP violating phase and Majorana phases for the
two types. The model parameters which are allowed by the experimental data of
the lepton mixing angles are different for each type. We also study the
constraints on the model parameters which are related to Majorana phases. The
different allowed regions of the model parameters for the two types are shown
numerically for a given region of two combinations of the CP violating phases.
