  In this paper, we make a detailed study on the hadronic production of the
$\Xi_{bc}$ baryon at a fixed target experiment at the LHC (After@LHC). In
estimating the production cross sections, the $(g+g)$, $(g+c)$ and $(g+b)$
production mechanisms are considered. For the initial heavy quarks, in addition
to the extrinsic component, we also consider the intrinsic component. It is
found that the $(g+c)$ and $(g+b)$ production mechanisms give sizable
contributions to the $\Xi_{bc}$ production, and the $(g+b)$ mechanism dominates
the production. The results show that there are about $3.40\times10^5$
$\Xi_{bc}$ events can be produced per year at After@LHC if the integrated
luminosity of After@LHC can be up to $2\,{\rm fb}^{-1}$ per year. Moreover, the
intrinsic heavy quarks can have significant impact on the production, which
inversely makes the intrinsic component be possibly tested at the After@LHC.
