We investigate a possibility for explaining the recently announced 750 GeV diphoton excess by the ATLAS and CMS experiments at the CERN Large Hadron Collider in a model with multiple doubly charged particles, that was originally suggested for explaining tiny neutrino masses through a three-loop effect in a natural way. The enhanced radiatively generated effective coupling of a new singlet scalar S with diphoton with multiple charged particles in the loop enlarges the production rate of S in pp → S +X via a photon fusion process and also the decay width Γ(S → γ γ ) even without assuming a tree-level production mechanism. We provide detailed analysis on the cases with or without allowing mixing between S and the standard model Higgs doublet. © The Author(s) 2016.