  In the framework of the littlest Higgs model with $T$ parity, we present
complete calculations for the $A_H q_-$ $(q_-=u_-, \bar{u}_-,d_-,
\bar{d}_-,c_-, \bar{c}_-,s_-, \bar{s}_-)$ associated production up to the QCD
next-to-leading order (NLO) at the CERN Large Hadron Collider with subsequent
pure weak decay of $T$-odd mirror quark. We apply the PROSPINO scheme to avoid
the double counting problem and to keep the convergence of the perturbative QCD
description. The theoretical correlations between the integrated cross section
and the factorization and renormalization scale, the global symmetry-breaking
scale and the Yukawa coupling parameter are studied separately. We also provide
the kinematic distributions of the final decay products. Our numerical results
show that the NLO QCD correction reduces the scale uncertainty and enhances the
leading-order integrated cross section remarkably, with the $K$ factor varying
in the range of $1.41 \sim 1.68$ ($1.58 \sim 1.89$) as the increment of the
global symmetry-breaking scale $f$ from $500~{\rm GeV}$ to $1.5~{\rm TeV}$
($1.1~{\rm TeV}$) at the $\sqrt{s} = 14~{\rm TeV}$ ($8~{\rm TeV}$) LHC. We find
that it is possible to select the signal events of the $A_Hq_-$ production from
its background by putting proper cuts on the final leading jet and missing
energy.
