We try to interpret a very light dark matter with mass of 5~10 GeV which is in favor of the recent experiments reported by CoGeNT and DAMA, in a non-supersymmetric extension of radiative seesaw model with a family symmetry D_6 x Z_2 x Z_2. We show that a D_6 singlet real scalar field can be a promising dark matter candidate, and it gives the elastic cross section sigma simeq 7x10^{-41} cm^2 which is required by these experiments. Our dark matter interacts with a D_6 singlet scalar Higgs boson, which couples only to quark sector. The dark matter-nucleon cross section and new decay mode h->DM DM can be large if the standard model Higgs boson h is light. The Higgs phenomenology is also discussed.
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