In this paper, we analyze the loop-induced decays of neutral Higgs boson h into pairs of photons, gluons and Z gamma in 3-Higgs Doublet Models (3HDMs), where all the doublets have nonzero vacuum expectation values. In the 3HDM, there are contributions to these decays from loops of charged scalars H-1,2(+/-) that are not present in the Standard Model. We find an enhancement in the channel h -> Z gamma with respect to the Standard Model prediction in some parameter region while respecting constraints from the measurements of h -> gamma gamma at the LHC. The charged Higgs bosons H-1,2(+/-) lead to the enhancement of Z gamma decay mode in some part of the parameter space of the 3HDM. Then, we discuss the correlations between the decay modes h -> Z gamma and h -> gamma gamma. Moreover, we study Type-I and Type-Z of 3HDMs and find that these types of 3HDMs can be distinguished via only the gluonic decays, since the contributions of the H-1,2(+/-) loops are dominant to those of fermion loops. We also investigate the effects of the model parameters on these loop-induced decays. As an interesting phenomenological consequence, the 3HDM is dominantly governed by the parameters: two ratios of vacuum expectation values (VEVs); tan gamma, tan beta and the mixing angles of the CP-even Higgs bosons, alpha(1,2) and theta.