By using the water-electrode discharge experimental setup, the white-eye hexagonal pattern is firstly observed and investigated in the dielectric barrier discharge with the mixture of argon and air whose content can be varied whenever necessary, and the study shows that the white-eye cell is an interleaving of three different hexagonal sub-structures: the spot, the ring, and the halo. The white-eye hexagonal pattern has the excellent discharge stability and sustainability during the experiment. Pictures recorded by ordinary camera with long exposure time in the same argon content condition show that the spot, the ring, and the halo of the white-eye hexagonal pattern have different brightness, which may prove that their plasma states are different. And, it is worth noting that there are obvious differences not only on the brightness but also on the color of the white-eye cell in conditions of different argon content, which shows that its plasma state also changed with the variation of the argon content. The white-eye hexagonal pattern is observed at a lower applied voltage so that the temperature of the water electrodes almost keeps unchanged during the whole experiment, which is advantageous for the long term stable measurement. The plasma state will not be affected by the temperature of the electrodes during the continuous discharge. Based on the above phenomena, plasma temperatures of the spot, the ring, and the halo in white-eye hexagonal pattern including molecule vibrational temperature and variations of electron density at different argon content are investigated by means of optical emission spectroscopy (OES). The emission spectra of the N2 second positive band(C3Πu→B3Πg)are measured, and the molecule vibrational temperature of the spot, the ring, and the halo of the white-eye hexagonal pattern are calculated by the emission intensities. Furthermore, emission spectra of Ar Ⅰ(2P2→1S5)is collected and the changes of its width with different argon content are used to estimate the variations of electron density of the spot, the ring, and the halo of the white-eye hexagonal pattern. In the same argon content condition, the molecule vibrational temperatures of halo, ring, and spot in the white-eye hexagonal pattern are in descending order, while the electron densities of halo, ring, and spot are in ascending order. With argon content increasing from 70% to 90%, both the molecule vibrational temperature and the electron density of the spot increase, while both of them of the halo decrease. And the molecule vibrational temperature of the ring keeps constant, while its electron density decreases. The experimental results indicate that the plasma state of the spot, the halo and the ring in a white-eye cell of the white-eye hexagonal pattern is different. These results are of great importance to the investigation of the multilayer structure of the patterns in dielectric barrier discharge and applications in industry.