  In unparticle dark matter (unmatter) models the equation of state of the
unmatter is given by $p=\rho/(2d_U+1)$, where $d_U$ is the scaling factor.
Unmatter with such equations of state would have a significant impact on the
expansion history of the universe. Using type Ia supernovae (SNIa), the baryon
acoustic oscillation (BAO) measurements and the shift parameter of the cosmic
microwave background (CMB) to place constraints on such unmatter models we find
that if only the SNIa data is used the constraints are weak. However, with the
BAO and CMB shift parameter data added strong constraints can be obtained. For
the $\Lambda$UDM model, in which unmatter is the sole dark matter, we find that
$d_U > 60$ at 95% C.L. For comparison, in most unparticle physics models it is
assumed $d_U<2$. For the $\Lambda$CUDM model, in which unmatter co-exists with
cold dark matter, we found that the unmatter can at most make up a few percent
of the total cosmic density if $d_U<10$, thus it can not be the major component
of dark matter.
