  We study the polarized $\Lambda_b$ baryon semileptonic decay $\Lambda_b \to
\Lambda_cl{\bar\nu}$ using perturbative QCD factorization theorem. In this
approach heavy baryon transition form factors are expressed as the convolutions
of hard $b$ quark decay amplitudes with universal $\Lambda_b$ and $\Lambda_c$
baryon wave functions. With the heavy baryon wave functions determined in our
previous work, we predict the asymmetry parameter $\alpha({\hat e})\equiv
(N_+-N_-)/(N_++N_-)=-0.31 {\bf P}\cdot{\hat e}$, where ${\bf P}$ is the
$\Lambda_b$ baryon polarization, ${\hat e}$ a unit vector perpendicular to the
$\Lambda_b$ baryon momentum, $N_+$ ($N_-$) the number of leptons whose momenta
possess positive (negative) components along ${\hat e}$. This result is useful
for extracting the transverse polarization of a $\Lambda_b$ baryon from data of
exclusive semileptonic decays.
