The evolution of filaments structure with the applied voltage and gas pressure in dielectric barrier discharge in argon/air mixture is studied, which is also analyzed in the aspect of two-dimensional phase transition. With the increase of the applied voltage, the filaments structure undergoes stages of sparse random filaments-dense random filaments-hexagon structure-hexagonal superlattice structure-chaos, which can be considered as a phase transition from gas-liquid-simple solid-superlattice solid-liquid. The changes of the lattice constant and the distance between two neighboring lattice points are investigated in the process of formation of the hexagonal superlattice structure in the phase transition. In addition, the formation of the large spots and the Penta-Hepta defects in the hexagonal superlattice structure are also studied.