  We investigate the Standard Model Higgs boson production in $e^-\gamma$
collision. The electroweak one-loop contributions to the scattering amplitude
for $e^-\gamma\rightarrow e^-H$ are calculated and expressed in analytical
form. We analyze the cross section for the Higgs production in $e^-\gamma$
collision for each combination of polarizations of the initial electron and
photon beams. The feasibility of observing the Higgs boson in
$e^-+\gamma\rightarrow e^-+b+{\overline b}$ channel is examined.
