  In the context of the littlest Higgs model, we study the associated
production of the Higgs boson and a top quark ($th$ production) at the CERN
Large Hadron Collider (LHC). The cross sections for s-channel, t-channel
processes and the relative correction for the total cross section are
presented. In a part of parameter space, the cross sections can be distinctly
deviated from the predictions of Standard Model. We also investigate the signal
and backgrounds for the $th$ production at the LHC. However, due to the large
QCD backgrounds, it is not very hopeful to directly observe the $th$ signal in
most of the parameter space of LH model. It is found that with 30 fb$^{-1}$ of
integrated luminosity, in a narrow range of the parameter space $c=0.8$ and
$f\leq 1.62$ TeV, a statistical significance of 3$\sigma$ can be achieved. More
than 30 fb$^{-1}$ luminosity will enhance the significance and the possibility
of detecting the signal.
