The model with lepton flavor non-universality can generate the active neutrino masses via the Zee mechanism, which predicts the existence of the charged Higgs bosons by introducing new free parameters and Mh where i, j denote e, μ, or τ. We calculate the contributions of to the , , and decays, and extract individual constraints on the factor /Mh by combining the current experimental measurements. We find that can provide more stringent constraints on /Mh than , while the obtained constraints on /Mh are comparable from these decays. The contributions of to the muon anomalous magnetic moment aμ and non-standard interactions of neutrinos are also discussed.