Unparticle with scaling dimension d_ has peculiar thermal properties due to its unique phase space structure. We find that the equation of state parameter ω_, the ratio of pressure to energy density, is given by 1/(2d_ +1) providing a new form of energy in our universe. In an expanding universe, the unparticle energy density ρ_(T) evolves dramatically differently from that for photons. For d_ >1, even if ρ_(T_D) at a high decoupling temperature T_D is very small, it is possible to have a large

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... elic density ρ_(T^0_γ) at present photon temperature T^0_γ, large enough to play the role of dark matter. We calculate T_D and ρ_(T^0_γ) using photon-unparticle interactions for illustration.