  We present a complete calculation of the QCD corrections (of the order
$\alpha_s$) to the width of the decay $H^+ \to t \bar{b}$ within the Minimal
Supersymmetric Standard Model. We find that the QCD corrections are quite
important, and that the supersymmetric QCD corrections (due to gluino, stop and
sbottom exchange) can be comparable to or even larger than the standard QCD
corrections in a large region of the supersymmetric parameter space. This is
mainly due to the effect of large left-right mixings of stop and sbottom. This
could significantly affect the phenomenology of the $H^+$ search.
