  We investigate quasinormal modes of a massless charged scalar field on a
small Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black hole both with
analytical and numerical approaches. In the analytical approach, by using the
small black hole approximation (r_+ << L), we obtain the quasinormal mode
frequencies in the limit of r_+/L -> 0, where r_+ and L stand for the black
hole event horizon radius and the AdS scale, respectively. We then show that
the small RN-AdS black hole is unstable if its quasinormal modes satisfy the
superradiance condition and that the instability condition of the RN-AdS black
hole in the limit of r_+/L -> 0 is given by Q>(3/eL)Q_c, where Q, Q_c, and e
are the charge of the black hole, the critical (maximum) charge of the black
hole, and the charge of the scalar field, respectively. In the numerical
approach, we calculate the quasinormal modes for the small RN-AdS black holes
with r_+ << L and confirm that the RN-AdS black hole is unstable if its
quasinormal modes satisfy the superradiance condition. Our numerical results
show that the RN-AdS black holes with r_+ =0.2L, 0.1L, and 0.01L become
unstable against scalar perturbations with eL=4 when the charge of the black
hole satisfies Q > 0.8Q_c, 0.78Q_c, and 0.76Q_c, respectively.
