  We calculate the contributions of the top-Higgs $h_{t}^{0}$ predicted by
topcolor assisted technicolor(TC2) models to $e^{+}e^{-}\longrightarrow
\overline{t}c\overline{\nu}_{e}\nu_{e}$ and compare the results with the
contributions of $h^{0}_{t}$ to the processes $e^{+}e^{-}\longrightarrow Z
h^{0}_{t}\longrightarrow Z\overline{t}c$ and $e^+e^-\longrightarrow \gamma
h^{0}_{t} \longrightarrow \gamma \overline{t}c$. We find that $e^{+}e^{-}
\longrightarrow\overline{t}c\overline{\nu}_{e}\nu_{e}$ is very sensitive to
$h^{0}_{t}$, which can be easy detected via this process at high-energy
$e^{+}e^{-}$ collider(LC) experiments with $\sqrt{s}\geq 500$ $GeV$, as long as
its mass below the $\overline{t}t$ threshold. The process $e^{+}e^{-}
\longrightarrow \gamma\overline{t}c$ also can be used to detect $h^{0}_{t}$ at
LC experiments.
