  We will show that the 3-3-1 model with new heavy right handed neutrinos as
$SU(3)_L$ singlets can explain simultaneously the lepton flavor violating
decays of the SM-like Higgs boson, charged lepton flavor violating decays
$e_b\rightarrow e_a\gamma$, and the electron $(g-2)_e$ anomalies under recent
experimental data. The discrepancy of $(g-2)_{\mu}$ 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 $h\to \tau e, \tau\mu$ can
reach the values of $\mathcal{O}(10^{-4})$.
