  The littlest $Higgs$ model with T-parity (called the $LHT$ model) predicts
the existence of the T-odd leptons, which can generate contributions to some
leptonic processes at the one-loop level. We calculate their contributions to
the leptonic $Z$ decay processes $Z\to l\bar{l'}$, $Z\to l\bar{l}$, and
$Z\rightarro \nu\bar{\nu}$. We find that the T-odd leptons can give significant
contributions to the branching ratios of these decay processes in most of the
parameter space. The experimental measurement values might generate constraints
on the free parameters of the $LHT$ model.
