Z-boson decay provides a good opportunity to search for the   $ \Xi_{bQ} $   baryon because a large number of its events can be collected at high energy colliders. In this paper, we perform a complete investigation of the indirect production of the   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $   baryons via the Z-boson decay process   $ \Xi_{bQ} $   with a   $ \Xi_{bQ} $   quark under the NRQCD factorization approach. After considering the contribution from the diquark states   $ \Xi_{bQ} $  ,   $ \Xi_{bQ} $  ,   $ \Xi_{bQ} $  , and   $ \Xi_{bQ} $  , the calculated branching fractions are   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $  . Furthermore, the   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $   production events are predicted to be of the order of   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $   at the LHC collider, and the order of   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $   for the CEPC collider. We then estimate the production ratio for   $ \Xi_{bQ} $   with   $ \Xi_{bQ} $   in Z-boson decay, that is,   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $  , respectively. Finally, we present the differential decay widths of   $ \Xi_{bQ} $   and   $ \Xi_{bQ} $   with respect to   $ \Xi_{bQ} $   and z distributions and analyze the uncertainties.