  In this paper, we study a stability problem of free boundary hypersurfaces,
and also capillary ones whose boundary supported on a horosphere in hyperbolic
space. We prove that umbilical hypersurfaces are only stable immersed capillary
hypersurfaces whose boundary supported on a horosphere. Using the same method,
we show that a totally geodesic hyperplane is only stable immersed type-II
hypersurface whose boundary supported on a horosphere.
