An extension of the two Higgs doublet model including inverse seesaw neutrinos and neutral Higgs bosons was constructed based on the A₄ symmetry in order to explain the recent neutrino oscillation data. This model can distinguish two well-known normal and inverted order schemes of neutrino data once both the effective masses mβ in tritium beta decays and mee in the neutrinoless double beta decay are observed. The lepton flavor violating decays of the charged leptons e_b → e_aγ , μ → 3e, the Standard Model-like Higgs boson decays h → e_ae_b, and the μ–e conversions in some nuclei are generated from loop corrections. The experimental data on the branching ratio Br(μ → eγ , 3e) predict that the upper bounds of Br(τ → μγ , eγ ) and Br(h → e_ae_b) are much smaller than the planned experimental sensitivities. In contrast, the μ–e conversions are promising signals for experiments.