  We investigate the virtual effects of vector unparticles in the Moller
scattering. We derive the analytic expression for scattering amplitudes with
unpolarized beams. We obtain 95% confidence level limits on the unparticle
couplings $\lambda_{V}$ and $\lambda_{A}$ with integrated luminosity of
$L_{int}=50, 500 fb^{-1}$ and $\sqrt{s}=100, 300$ and 500 GeV energies. We show
that limits on $\lambda_{V}$ are more sensitive than $\lambda_{A}$.
