  We study a three loop induced neutrino mass model with exotic vector-like
isospin doublet leptons which contain a dark matter candidate. Then we explore
lepton flavor violations, and dark matter physics in co-annihilation system. In
this paper the nearly degenerate Majorana fermion dark matter can naturally be
achieved at the two loop level, while the mass splitting can be larger than
${\cal O}$(200) keV which is required from the constraint of the direct
detection search with spin independent inelastic scattering through $Z$ boson
portal. As a result a monochromatic photon excess, its threshold energy is
greater than ${\cal O}$(200) keV, is predicted in our model that could be
measured through indirect detection experiments such as INTEGRAL.
