  We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model
which is based on the nonextentive statistical mechanics. This new statistics
is characterized by a dimensionless nonextensivity parameter $q$ that accounts
for all possible effects violating the assumptions of the Boltzmann-Gibbs (BG)
statistics (when $q\rightarrow1$, it returns to the BG case). Based on the
nonextensive Polyakov-Nambu-Jona-Lasinio model, we discussed the influence of
the nonextensive effects on the QCD phase transition, especially on the
location of the critical end point (CEP). A new and interesting phenomenon we
found is that with the increase of $q$, the CEP position initially shifted
toward the direction of larger chemical potential and lower temperature. But
then, when $q$ is greater than a critical value $q_{c}$, the CEP position moves
in the opposite direction. In other words, as $q$ increases, the CEP position
moves in the direction of smaller chemical potential and higher temperature. In
addition, we calculated the influence of the nonextensive effects on the
critical exponents and found that they remain almost constant with $q$.
