  In the context of the littlest Higgs(LH) model, we study single production of
the new gauge bosons $B_{H}$, $Z_{H}$ and $W_{H}^{\pm}$ via $e^{-}\gamma$
collisions and discuss the possibility of detecting these new particles in the
$TeV$ energy $e^{+}e^{-}$ collider($LC$). We find that these new particles can
not be detected via the $e^{-}\nu\nu$ signal in all of the parameter space
preferred by the electroweak precision data. However, the heavy gauge bosons
$B_{H}$ and $Z_{H}$ may be observed via the decay channel $B_{H}(Z_{H})\to
l^{+}l^{-}$ in wide range of the parameter space.
