Gravitational perturbations of anti-de Sitter (AdS) spacetime play importan
t roles in the AdS conformal field theory correspondence and the brane worl
d scenario. In this paper, we develop a gauge-invariant formalism of gravit
ational perturbations of maximally symmetric spacetimes including anti-de S
itter spacetime. The existence of scalar-type master variables is shown and
the corresponding master equations are derived.