  The doubly heavy baryon $\Xi_{QQ^{\prime}}$ ($Q^{(\prime)}$ = $b$ or $c$) is
different from the ordinary baryons. The production of the doubly heavy baryon
can provide valuable insight on how the colored $(QQ^{\prime})$-diquark can be
transformed into the color-singlet baryon. As a sequential work of Ref.[2], we
make a further study on the doubly heavy baryon production through the $e^+
e^-$ annihilation channel, $e^{+} + e^{-}\rightarrow\gamma/Z^0 \rightarrow
\Xi_{QQ^{\prime}} +\bar{Q} +\bar{Q^{\prime}}$, within the nonrelativistic QCD
framework. In addition to the total cross sections, we present the baryon
transverse momentum and the rapidity distributions for all these channels.
Typical baryon transverse momentum and rapidity cuts are adopted to show the
properties of these distributions clearly. At a $e^+ e^-$ collider that runs
around the $Z^0$-boson mass with a high luminosity up to ${\cal L} =
10^{34-36}{\rm cm}^{-2} {\rm s}^{-1}$, in comparison to the Belle and BABAR
experiments, it is found that sizable $\Xi_{cc}$, $\Xi_{bc}$ and $\Xi_{bb}$
events can be produced even after performing baryon's transverse momentum and
rapidity cuts due to $Z^0$-boson resonance effect.
