From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature T and baryon chemical potential μB in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, q, and the results in the usual Boltzmann-Gibbs case are recovered when q→1. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature Tc is shown to decrease with increasing q from the phase diagram in the (T,μ) plane. However, larger values of q cause the rise of Tc at low temperature but high chemical potential. Moreover, it is found that μ different from zero corresponds to a first-order phase transition while μ=0 to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with q increasing due to the nonextensive effects.