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