  We discuss a possibility to explain the 750 GeV diphoton excess observed at
the LHC in a three-loop neutrino mass model which has a similar structure to
the model by Krauss, Nasri and Trodden. Tiny neutrino masses are naturally
generated by the loop effect of new particles with their couplings and masses
to be of order 0.1-1 and TeV, respectively. The lightest right-handed neutrino,
which runs in the three-loop diagram, can be a dark matter candidate. In
addition, the deviation in the measured value of the muon anomalous magnetic
moment from its prediction in the standard model can be compensated by one-loop
diagrams with exotic multi-charged leptons and scalar bosons. For the diphoton
event, an additional isospin singlet real scalar field plays the role to
explain the excess by taking its mass of 750 GeV, where it is produced from the
gluon fusion production via the mixing with the standard model like Higgs
boson. We find that the cross section of the diphoton process can be obtained
to be a few fb level by taking the masses of new charged particles to be about
375 GeV and related coupling constants to be order 1.
