  The littlest Higgs model with discrete symmetry named "T-parity"(LHT) is an
interesting new physics model which does not suffer strong constraints from
electroweak precision data. One of the important features of the LHT model is
the existence of new source of FC interactions between the SM fermions and the
mirror fermions. These FC interactions can make significant loop-level
contributions to the couplings $tcV$, and furthermore enhance the cross
sections of the FC single-top quark production processes. In this paper, we
study some FC single-top quark production processes, $pp\to t\bar{c}$ and
$pp\to tV$, at the LHC in the LHT model. We find that the cross sections of
these processes are strongly depended on the mirror quark masses. The processes
$pp\to t\bar{c}$ and $pp\to tg$ have large cross sections with heavy mirror
quarks. The observation of these FC processes at the LHC is certainly the clue
of new physics, and further precise measurements of the cross scetions can
provide useful information about the free parameters in the LHT model,
specially about the mirror quark masses.
