We consider dark matter physics in a model for the dark sector with extra dark U(1)X gauge symmetry. The dark sector is composed of exotic fermions that are charged under both dark U(1)X and the standard model SU(3)C×U(1)Y gauge groups, as well as standard model singlet complex scalars Φ and X with nonzero U(1)X charge. In this model, there are two dark matter candidates-a scalar and a fermion-both of which are stabilized by accidental Z2 symmetry. Their thermal relic density, and direct and indirect detection constraints are discussed in detail and we search for the parameter space of the model accommodating dark matter observations. We also discuss constraints from diphoton resonance searches associated with the scalar field which breaks the dark U(1)X, in a way consistent with dark matter physics. In addition, implications for collider physics are discussed, focusing on the production cross section of the scalar boson.