We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model that is based on nonex-tentive statistical mechanics.This new statistics model is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs (BG) statistics (for q → 1,it returns to the BG case).Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model,we discussed the influ-ence of nonextensive effects on the curvature of the phase diagram at μ =0 and especially on the location of the crit-ical end point (CEP).A new and interesting phenomenon we found is that with an increase in q,the CEP position initially shifts toward the direction of larger chemical potential and lower temperature.However,when q is larger than a critical value qc,the CEP position moves in the opposite direction.In other words,as q increases,the CEP po-sition moves in the direction of smaller chemical potential and higher temperature.This U-turn phenomenon may be important for the search of CEP in relativistic heavy-ion collisions,in which the validity of BG statistics is question-able due to strong fluctuations and long-range correlations,and nonextensive effects begin to manifest themselves.In addition,we calculated the influence of the nonextensive effects on the critical exponents and found that they re-main almost constant with q.