  We study the stability of AdS black hole holes rotating in a single two plane
for tensor-type gravitational perturbations in $D > 6$ space-time dimensions.
First, by an analytic method, we show that there exists no unstable mode when
the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$
is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical
calculations of quasinormal modes, using the separability of the relevant
perturbation equations, we show that an instability occurs for rapidly rotating
black holes with $a>r_h^2/R$, although the growth rate is tiny (of order
$10^{-12}$ of the inverse horizon radius). We give numerical evidences
indicating that this instability is caused by superradiance.
