  We investigate the structure and stability of the thermal equilibrium states
of a spherically symmetric self-gravitating system in a $D$-dimensional
asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the
Einstein-Vlasov equations with a negative cosmological constant. Due to the
confined structure of the AdS potential, we can construct thermal equilibrium
states without any artificial wall in the asymptotically AdS spacetime.
Accordingly, the AdS radius can be regarded as the typical size of the system.
Then the system can be characterized by the gravothermal energy and AdS radius
normalized by the total particle number. We investigate the catastrophic
instability of the system in a $D$-dimensional spacetime by using the turning
point method. As a result, we find that the curve has a double spiral structure
for $4\le D\le 10$ while it does not have any spiral structures for $D\ge11$ as
in the asymptotically flat case confined by an adiabatic wall. Irrespective of
the existence of the spiral structure, there exist upper and lower bounds for
the value of the gravothermal energy. This fact indicates that there is no
thermal equilibrium solution outside the allowed region of the gravothermal
energy. This property is also similar to the asymptotically flat case.
