  We present a comprehensive study of the massless scalar field perturbation in
the Reissner-Nordstrom anti-de Sitter (RNAdS) spacetime and compute its
quasinormal modes (QNM). For the lowest lying mode, we confirm and extend the
dependence of the QNM frequencies on the black hole charge got in previous
works. In near extreme limit, under the scalar perturbation we find that the
imaginary part of the frequency tends to zero, which is consistent with the
previous conjecture based on electromagnetic and axial gravitational
perturbations. For the extreme value of the charge, the asymptotic field decay
is dominated by a power-law tail, which shows that the extreme black hole can
still be stable to scalar perturbations. We also study the higher overtones for
the RNAdS black hole and find large variations of QNM frequencies with the
overtone number and black hole charge. The nontrivial dependence of frequencies
on the angular index is also discussed.
