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By adding new gauge singlets of neutral leptons, the improved versions of the3-3-1 models with right-handed neutrinos have been recently introduced in orderto explain recent experimental neutrino oscillation data through the inverseseesaw mechanism. We prove that these models predict promising signals oflepton-flavor-violating decays of the standard-model-like Higgs boson$h^0_1\rightarrow \mu\tau,e\tau$, which are suppressed in the originalversions. One-loop contributions to these decay amplitudes are introduced inthe unitary gauge. Based on a numerical investigation, we find that thebranching ratios of the decays $h^0_1\rightarrow\mu\tau,e\tau$ can reach valuesof $10^{-5}$ in the regions of parameter space satisfying the currentexperimental data of the decay $\mu\rightarrow e\gamma$. The value of $10^{-4}$appears when the Yukawa couplings of leptons are close to the perturbativelimit. Some interesting properties of these regions of parameter space are alsodiscussed.

Decay of standard model-like Higgs boson $h\rightarrow \mu\tau$ in a 3-3-1 model with inverse seesaw neutrino masses