Unparticle $U$ with scaling dimension $d_U$ has peculiar thermal properties due to its unique phase space structure. We find that the equation of state parameter $omega_U$, the ratio of pressure to energy density, is given by $1/(2d_U +1)$ providing
a new form of energy in our universe. In an expanding universe, the unparticle energy density $rho_U(T)$ evolves dramatically differently from that for photons. For $d_U >1$, even if $rho_U(T_D)$ at a high decoupling temperature $T_D$ is very small, it is possible to have a large relic density $rho_U(T^0_gamma)$ at present photon temperature $T^0_gamma$, large enough to play the role of dark matter. We calculate $T_D$ and $rho_U(T^0_gamma)$ using photon-unparticle interactions for illustration.
