Square super-lattice pattern with surface discharge consisting of central spots and dim spots is firstly observed in the mixture of argon and air by using a dielectric barrier discharge device with water electrodes. By observing the image, it is found that the central spot is located at the centriod of its surrounding four dim spots. The short-exposure image recorded by a high speed video camera shows that the dim spot results from the surface discharges (SDs). The brightness of the central spot and is quite different from that of the dim spot, which indicates that the plasma states of the central spot and the dim spot may be differentiated. The optical emission spectrum method is used to further study the several plasma parameters of the central spot and the dim spot in different argon content. The emission spectra of the N2 second positive band (C3Πu→B3Πg) are measured, from which the molecule vibration temperatures of the central spot and the dim spot are calculated respectively. The broadening of spectral line 696.57 nm (2P2→1S5) is used to study the electron densities of the central spot and the dim spot. It is found that the molecule vibration temperature and electron density of the dim spot are higher than those of the central spot in the same argon content. The molecule vibration temperature and electron density of the central spot and the dim spot increase with the argon content increasing from 90% to 99.9%. The surface discharge induced by the volume discharge (VD) has the determinative effect on the formation of the dim spot. The experimental results above play an important role in studying the formation mechanism of surface discharge of square super-lattice pattern with surface discharge. In addition, the studies exert an influence on the application of surface discharge and volume discharge in different fields.