  The dirac quasinormal modes of the Reissner-Nordstr\"om black hole surrounded
by quintessence are investigated using the third WKB approximation. We find
that the magnitude of the imaginary part of the quasinormal mode frequencies
increases firstly and then decreases as the charge $Q$ increases, but it
decreases as the absolute value of $w_{q}$ increases. The magnitude of the
imaginary part of quasinormal complex frequencies is smaller than those with no
quintessence. That is to say, the dirac field damps more slowly due to the
presence of quintessence.
