A new type of hexagonal superlattice pattern is observed under three different boundary conditions by using a dielectric barrier discharge device with water electrode. The power spectrum of hexagonal superlattice pattern and its angular distributions are shown. The phase diagram of the hexagonal superlattice pattern as a function of air concentration and applied voltage is obtained. The correlation measurements indicate that the hexagonal superlattice pattern is an interllacing of two different transient sublattices. The selection of pattern formation in quadrangular boundary with different area is studied. It is found that the hexagonal superlattice pattern is a typical type of nonlinear self-organized pattern, and the formation of square superlattice pattern is dependent upon the boundary conditions.