  The new lightest gauge boson $B_H$ with mass of a few hundred GeV is
predicted in the littlest Higgs model. $B_H$ should be accessible in the planed
ILC and the observation of such particle can strongly support the littlest
Higgs model. The realization of $\gamma\gamma$ and $e\gamma$ collision will
open a wider window to probe $B_H$. In this paper, we study the new gauge boson
$B_{H}$ production processes $e^{-}\gamma\to e^{-}\gamma B_{H}$ and
$e^{-}\gamma\to e^{-}Z B_{H}$ at the ILC. Our results show that the production
cross section of the process $e^{-}\gamma\to e^{-}Z B_{H}$ is less than one fb
in the most parameter spaces while the production cross section of the process
$e^{-}\gamma\to e^{-}\gamma B_{H}$ can reach the level of tens fb and even
hundreds of fb in the sizable parameter spaces allowed by the electroweak
precision data. With the high luminosity, the sufficient typical signals could
be produced, specially via $e^{-}\gamma\to e^{-}\gamma B_{H}$. Because the
final electron and photon beams can be easily identified and the signal can be
easily distinguished from the background produced by $Z$ and $H$ decaying,
$B_H$ should be detectable via $e\gamma$ collision at the ILC. Therefore, the
processes $e^{-}\gamma\to e^{-}\gamma B_{H}$ and $e^{-}\gamma\to e^{-}Z B_{H}$
provide a useful way to detect $B_{H}$ and test the littlest Higgs model.
