  In this work we give a comprehensive analysis on the phenomenology of a
specific $\mathbb{Z}_3$ dark matter (DM) model in which neutrino mass is
induced at two loops by interactions with a DM particle that can be a complex
scalar or a Dirac fermion. Both the DM properties in relic density and direct
detection and the LHC signatures are examined in great detail, and indirect
detection for gamma-ray excess from the Galactic Center is also discussed
briefly. On the DM side, both semi-annihilation and co-annihilation processes
play a crucial role in alleviating the tension of parameter space between relic
density and direct detection. On the collider side, new decay channels
resulting from $\mathbb{Z}_3$ particles lead to distinct signals at LHC.
Currently the trilepton signal is expected to give the most stringent bound for
both scalar and fermion DM candidates, and the signatures of fermion DM are
very similar to those of electroweakinos in simplified supersymmetric models.
