  Due to the presence of extra top quark T in the little Higgs models, the
$CKM$ matrix is not unitary and the flavor changing neutral currents may exist
at the tree level. In the context of the Littlest Higgs(LH) model, we discuss
the top-charm production at the high-energy linear $e^{+}e^{-}$ collider $(LC)$
via the processes $e^{+}e^{-}\to \bar{t}c +t\bar{c}$, $e^{+}e^{-}\to (\bar{t}c
+t\bar{c})\nu_{e}\bar{\nu_{e}}$, and $e^{-}\gamma\to e^{-}\bar{t}c$. We find
that the resonance production cross section for the process $e^{+}e^{-}\to
\bar{t}c+ t\bar{c} $ is significantly larger, which can be detected in future
$LC$ experiments.
