Abstract: The critical exponents at the Critical end Point(CEP) and the spinodal boundaries are investigated in the Poyakov-Nambu--Jona-Lasinio(PNJL) model. The numerical results show that the four standard critical exponents, \alpha, \beta, \gamma and \delta, are consistent with Landau-Ginzburg theory in the mean-field approximation. The critical exponent \eta ~(\approx2) correlated to kurtosis is larger than the critical exponent \zeta~(\approx1) of skewness at the CEP, which indicates that the measurement of kurtosis is more sensitive than skewness if the critical region can be reached in heavy-ion collision. The calculation also shows that the critical exponent of skewness~(kurtosis) along the spinodal line has the same divergent strength as that at the CEP. Due to the violent fluctuations in the unstable and metastable phases and the divergence of skewness and kurtosis at the spinodal boundaries, the signals to identify the first-order transition in the future experiments will be disturbed to a certain degree. Some deviations from the prediction of standard first-order transition may be found in observation.