The Large Hadron Collider (LHC) is anticipated to provide signals of new physics at the TeV scale, which are likely to involve production of a weakly interacting massive particle dark matter candidate. The International Linear Collider (ILC) is to sort out these signals and lead us to some viable model of the new physics at the TeV scale. In this article, we discuss how the ILC can discriminate new physics models, taking the following three examples: the inert Higgs model, the supersymmetric model, and the littlest Higgs model with T-parity. These models predict dark matter particles with different spins, 0, 1/2, and 1, respectively, and hence comprise representative scenarios. Specifically, we focus on the pair production process, e⁺e⁻ → x⁺x⁻ → x⁰x⁰W⁺W⁻, where x⁰ and x^± are the weakly interacting massive particle dark matter and a new charged particle predicted in each of these models. We then evaluate how accurately the properties of these new particles can be determined at the ILC and demonstrate that the ILC is capable of identifying the spin of the new charged particle and discriminating these models.