  The new colored vector-like heavy fermion $T$ is a crucial prediction in
little Higgs models, which plays a key role in breaking the electroweak
symmetry. The littlest Higgs model is the most economical one among various
little Higgs models. In the context of the littlest Higgs model, we study
single production of the new heavy vector-like quark via $e^{-}\gamma$
collisions and discuss the possibility of detecting this new particle in the
TeV energy $e^{+}e^{-}$ collider(LC). We find that the production cross section
can vary in a wide range($10^{-3}-10^{1}fb$) in most parameter spaces. For the
favorable parameter spaces, the possible signals of the vector-like top quark
$T$ can be detected via $e^{-}\gamma$ collisions in future $LC$ experiment with
$\sqrt{s}=3TeV$ and $\pounds=500fb^{-1}$.
