We will show that the 3-3-1 model with new heavy right-handed neutrinos as SU(3)_L singlets can simultaneously explain the lepton flavor violating decays of the SM-like Higgs boson, charged lepton flavor violating decays e_b → e_aγ , and the electron (g − 2)_e anomalies under recent experimental data. The discrepancy of (g − 2)_μ predicted by the model under consideration and that of the standard model can reach 10^-9. The decay rates of the standard model-like Higgs boson h → τ e,τμ can reach values of O(10^-4 ).