  In the framework of the improved version of the 3-3-1 models with
right-handed neutrinos, which is added to the Majorana neutrinos as new gauge
singlets, the recent experimental neutrino oscillation data is completely
explained through the inverse seesaw mechanism. We show that the major
contributions to $Br(\mu\rightarrow e\gamma)$ are derived from corrections at
1-loop order of heavy neutrinos and bosons. But, these contributions are
sometime mutual destructive, creating regions of parametric spaces where the
experimental limits of $Br(\mu\rightarrow e\gamma)$ are satisfied. In these
regions, we find that $Br(\tau\rightarrow \mu\gamma)$ can achieve values of
$10^{-10}$ and $Br(\tau\rightarrow e\gamma)$ may even reach values of $10^{-9}$
very close to the upper bound of the current experimental limits. Those are
ideal areas to study lepton-flavor-violating decays of the standard model -like
Higgs boson ($h_1^0$). We also pointed out that the contributions of heavy
neutrinos play an important role to change $Br(h_1^0\rightarrow \mu\tau)$, this
is presented through different forms of mass mixing matrices ($M_R$) of heavy
neutrinos. When $M_R \sim diag(1,1,1)$, $Br(h_1^0\rightarrow \mu\tau)$ can get
a greater value than the cases $M_R \sim diag(1,2,3)$ and $M_R \sim
diag(3,2,1)$ and the largest that $Br(h_1^0\rightarrow \mu\tau)$ can reach is
very close $10 ^{-3}$.
