Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condi-tion and latent heat of phase transition for non-linear charged AdS black holes using Maxwell\'s equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T＜Tc)is re-lated to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we dis-cuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.