Two kinds of rhombus patterns consisted of the bright spot and dim spot were firstly observed and investigated in discharge of gas mixture of air and argon by using the dielectric barrier discharge device with double water electrodes. It was found that dim spot was at the center of four surrounding bright spots in the first kind of rhombus pattern (named rhombus pattern Ⅰ) and the dim spot is at the geometric gravity center of three surrounding bright spots in the second kind of rhombus pattern (named rhombus patternⅡ) by observing the discharge images. The optical emission spectrum method was used to study the several plasma parameters of two kinds of rhombus patterns. The emission spectra of the N2 second positive band（C3Πu→B3Πg） were measured, and the molecule vibration temperature was calculated by the emission intensities. The broadening of spectral line 696.54 nm（2P2→1S5）was used to study the electron densities. The experiment results show that the molecule vibration temperature of the dim spot is higher than that of the bright spot in the two kinds of rhombus patterns, and the molecule vibration temperature and electron densities of the bright spot and dim spot both increase from rhombus patternⅠ to rhombus patternⅡ, while the electron density of the dim spot is lower than that of the bright spot in the rhombus patternⅠ and the electron densities are almost equal in the rhombus patternⅡ. Because the electron densities presents different change trends in two kinds of rhombus patterns, so the short-exposure images were recorded by a high speed video camera and the results show that the dim spot resulting from the volume discharge and surface discharge co-exist in the rhombus patternⅡ. Further study of the electron densities of bright spot of three kinds of patterns found that the hightest was the prepattern of the rhombus patternⅡ and the lowest was the rhombus patternⅡ. These results are of great importance to the formation of the patterns in dielectric barrier discharge.