  We investigate a Z3 symmetric model with two-loop radiative neutrino masses.
Dark matter in the model is either a Dirac fermion or a complex scalar as a
result of an unbroken Z3 symmetry. In addition to standard annihilation
processes, semi-annihilation of the dark matter contributes to the relic
density. We study the effect of the semi-annihilation in the model and and that
those contributions are important to obtain the observed relic density. The
experimental signatures in dark matter searches are also discussed, where some
of them are expected to be different from the signatures of dark matter in Z2
symmetric models.
