  Inspired by the recent LHC Higgs data and null search results of
supersymmetry (SUSY), we scan the parameter space of the Minimal Supersymmetric
Standard Model (MSSM) with relatively heavy sparticles (1-3 TeV). Then in the
parameter space allowed by current collider experiments and dark matter
detections, we calculate the complete one-loop SUSY QCD corrections to $pp\to
b\bar{b}h$ at the LHC with $\sqrt{s}=14$ TeV and obtain the following
observations: (i) For the large values of $\tan\beta$ and low values of
$m_{A}$, the SUSY QCD effects can be quite large, which, however, have been
excluded by the latest results of LHC search for $H/A \to \tau^{+}\tau^{-}$;
(ii) For modest values of $\tan\beta$ and $m_{A}$ which so far survived all
experimental constraints, the SUSY QCD corrections can maximally reach about
-9%.
