  The $Z$-boson decay provides good opportunities for the research on
$\Xi_{bQ'}$ baryon due to large quantity of $Z$ events that can be collected at
the high-energy colliders. We performed a completed investigation of the
indirect production of the $\Xi_{bc}$ and $\Xi_{bb}$ baryon via $Z$-boson decay
$Z\to \Xi_{bQ'}+\bar b +\bar Q'$ with $Q'= (c, b)$ quark according to NRQCD
factorizations approach. After considering the contribution of the diquark
states $\langle bc\rangle [^3S_1]_{\bar 3/6}$, $\langle bc\rangle [^1S_0]_{\bar
3/6}$, $\langle bb\rangle [^1S_0]_{6}$ and $\langle bb\rangle [^3S_1]_{\bar
3}$, the calculated branching ratio for $Z\to\Xi_{bQ'}+X$ are ${\cal
B}(Z\to\Xi_{bc}+X) = 3.595\times 10^{-5}$ and ${\cal B}(Z\to\Xi_{bc}+X) =
1.213\times 10^{-6}$. Moreover, the $\Xi_{bc}$ events produced are predicted to
be of the $10^4(10^7)$ order at the LHC(CEPC), while the $\Xi_{bb}$ events
produced are forecasted to be of the $10^3(10^6)$ order. Furthermore, we have
estimated the production ratio ${\cal R}(Z_Q\to\Xi^{+,0}_{bc})$ with four
$Z$-boson decay channels. The ${\cal R}(Z_Q\to\Xi^{+,0}_{bc})$ up to $10^{-6}$
for $Z\to c\bar c$ channel and $10^{-5}$ for $Z\to b\bar b$ channel,
respectively. Finally, we present the differential decay widths of
$\Xi_{bc}(\Xi_{bb})$ with respect to $s_{23}$ and $z$ distributions, and
analysis the uncertainties.
