  We calculate NLO QCD corrections to the lightest neutral Higgs boson
production associated with top quark pair at hadron colliders in the minimal
supersymmetric standard model(MSSM). Our calculation shows that the total QCD
correction significantly reduces its dependence on the
renormalization/factorization scale. The relative correction from the SUSY QCD
part approaches to be a constant, if either $M_S$ or $m_{\tilde{g}}$ is heavy
enough. The corrections are generally moderate(in the range of few percent to
20%) and under control in most of the SUSY parameter space. The relative
correction is obviously related to $m_{\tilde{g}}$, $A_t$ and $\mu$, but not
very sensitive to $\tan\beta$, $M_S$ at both the Tevatron and the LHC with our
specified parameters.

High Energy Physics - Phenomenology