  We consider the perturbation of giant gravitons in the background of
dilatonic D-branes whose geometry is not of a conventional form of ${\rm AdS}_m
\times {\rm S}^n$. We use the quadratic approximation to the brane action to
investigate their vibrations around the equilibrium configuration. We found the
normal modes of small vibrations of giant gravitons and these vibrations are
turned out to be stable.
