  We predict the branching ratios of the lepton flavor violating Z boson decays
Z\to e^{\pm} \mu^{\pm}, Z\to e^{\pm} \tau^{\pm} and Z\to \mu^{\pm} \tau^{\pm}
in the case that the lepton flavor violation is carried by the scalar
unparticle mediation. We observe that their BRs are strongly sensitive to the
unparticle scaling dimension and the branching ratios can reach to the values
of the order of 10^{-8}, for the heavy lepton flavor case, for the small values
of the scaling dimension.
