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We discuss a supersymmetric model with discrete flavor symmetry $A_4\timesZ_3$. The additional scalar fields which contribute masses of leptons in theYukawa terms are introduced in this model. We analyze their scalar potentialand find that they have various vacuum structures. We show the relations among24 different vacua and classify them into two types. We derive expressions ofthe lepton mixing angles, Dirac CP violating phase and Majorana phases for thetwo types. The model parameters which are allowed by the experimental data ofthe lepton mixing angles are different for each type. We also study theconstraints on the model parameters which are related to Majorana phases. Thedifferent allowed regions of the model parameters for the two types are shownnumerically for a given region of two combinations of the CP violating phases.

Phenomenological Aspects of Possible Vacua of a Neutrino Flavor Model