  We evaluate the quasinormal modes of massless Dirac perturbation in a
Schwarzschild black hole surrounded by the free static spherically symmetric
quintessence by using the third-order WKB approximation. The result shows that
due to the presence of quintessence, the massless field damps more slowly. The
real part of the quasinormal modes increases and the the absolute value of the
imaginary part increases when the state parameter $w_q$ increases. In other
words, the massless Dirac field decays more rapidly for the larger $w_q$. And
the peak value of potential barrier gets higher as $|k|$ increases and the
location of peak moves along the right for fixed $w_q$.
