  The analytic expressions for the production cross sections of polarized
bottom and top quarks in $e^+e^-$ annihilation are explicitly derived at the
one-loop order of strong interactions. Chirality-violating mass effects will
reduce the longitudinal spin polarization for the light quark pairs by an
amount of $3\%$, when one properly considers the massless limit for the final
quarks. Numerical estimates of longitudinal spin polarization effects in the
processes $e^+e^-\to b\bar{b}(g)$ and $e^+e^- \to t\bar{t}(g)$ are presented.
