  In the simplest little Higgs model the new flavor-changing interactions
between heavy neutrinos and the Standard Model leptons can generate
contributions to some lepton flavor violating decays of $Z$-boson at one-loop
level, such as $Z \to \tau^{\pm}\mu^{\mp}$, $Z\to \tau^{\pm}e^{\mp}$, and $Z
\to \mu^{\pm}e^{\mp}$. We examine the decay modes, and find that the branching
ratios can reach $10^{-7}$ for the three decays, which should be accessible at
the Giga$Z$ option of the ILC.
