  The quasinormal modes (QNMs) of Dirac field perturbations of a
Reissner-Nordstr\"om black hole in an asymptotically Anti-de Sitter spacetime
are investigated. We find that both the real and imaginary parts of the
fundamental quasinormal frequencies for large black holes are the linear
functions of the Hawking temperature, and the slope of the lines for the real
parts decreases while that for the magnitude of the imaginary parts increases
as the black hole charge increases. According to the Anti-de Sitter/Conformal
Field Theory (AdS/CFT) correspondence, the fact shows that different charge
presents different time scale in three-dimensional CFT. Another interesting
result is that the quasinormal frequencies become evenly spaced for high
overtone number, and in the spacing expressions the real part decreases while
the magnitude of the imaginary part increases as the charge increases. We also
study the relation between quasinormal frequencies and angular quantum number
and find that the real part increases while the magnitude of the imaginary part
decreases as the angular quantum number increases.
