  We consider models with extra U(1)' gauge symmetry that is broken
spontaneously. In the models, there are cold dark matter candidates which are
charged under U(1)' symmetry. Depending on the charge assignment, we can evade
the strong bound from the Drell-Yang process, and consider the scenario that
the dark matters strongly interact with the fermions in the Standard Model
through the extra gauge boson exchanging. As an illustrative example, we
discuss a supersymmetric gauged U(1)_B \times U(1)_L model and see that not
only correct relic density but also the DAMA/CoGeNT excess can be achieved by
the dark matters.
