  The littlest Higgs model is the most economical one among various little
Higgs models. In the context of the littlest Higgs(LH) model, we study the
process $e^{-}\gamma\to \nu_{e}W^{-}H$ and calculate the contributions of the
LH model to the cross section of this process. The results show that, in most
of parameter spaces preferred by the electroweak precision data, the value of
the relative correction is larger than 10%. Such correction to the process
$e^{-}\gamma\to \nu_{e}W^{-}H$ is large enough to be detected via $e^{-}\gamma$
collisions in the future high energy linear $e^{+}e^{-}$ collider($LC$)
experiment with the c.m energy $\sqrt{s}$=500 GeV and a yearly integrated
luminosity $\pounds=100fb^{-1}$, which will give an ideal way to test the
model.
