  We calculate the QCD corrections to the cross section of e^+ e^- -> t anti-b
H^- and its charge-conjugate counterpart within the minimal supersymmetric
extension of the Standard Model. This process is particularly important if m_t
< m_H + m_b and root(s) < 2 m_H, so that t -> b H^+ and e^+ e^- -> H^+ H^- are
not allowed kinematically. Large logarithmic corrections that arise in the
on-mass-shell scheme of quark mass renormalization, especially from the t
anti-b H^- Yukawa coupling for large values of tan(beta), are resummed by
adopting the modified minimal-subtraction scheme, so that the convergence
behavior of the perturbative expansion is improved. The inclusion of the QCD
corrections leads to a significant reduction of the theoretical uncertainties
due to scheme and scale dependences.
