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In a 3-3-1 model with inverse seesaw neutrinos, we use a simple form of Higgspotential to give four CP-even Higgs bosons ($H \equivh^0_1,h^0_2,h^0_3,h^0_4$). We investigate $H \rightarrow \mu \tau$ decays inthe parameter space regions satisfying the experimental limits of $l_a\rightarrow l_b \gamma$ with running parameters being the mass of the chargedHiggs boson ($m_{H_1^\pm}$) and the mixing matrix of the heavy neutrinos($M_R$). We show that there exist regions of parameter space where all partialwidths $\Gamma (H \rightarrow \mu \tau)$ are less than the current experimentallimit ($4.1 \times 10^{-6} GeV$). Analyzing the contributing components to$\Gamma (H \rightarrow \mu \tau)$, we also compare the mass of the SM-likeHiggs boson with the corresponding ones of the other CP-even Higgs bosons inthis model.

Investigation of CP-even Higgs bosons decays $H \rightarrow \mu \tau$  within constraints of $l_a \rightarrow l_b \gamma$ in a 3-3-1 model with  inverse seesaw neutrinos