The dielectric barrier discharge are often generated in open air. In our system, the barrier discharge system is put into the solution of water and glycerine. The gas bubble is placed at one of the electrodes and the filamentary discharge is developed parallel to the electric field. Because large amount of charged particles accumulate at the head of the discharge, the electric field is enhanced in the vicinity of the region. As a result, the field polarizes the liquid and attracts the dipoles to form a concave shape at the head of a bubble. Such a phenomenon is called a Taylor cone. After the Taylor cone is formed, the discharge tends to propagate toward the electrode, which leads to the elongation and deformation of the bubble. On the other side, the discharge propagates at positive half cycles toward the anode. When the discharge arrives to the dielectric layer, the pressure in the bubble near the anode is suddenly increased. Gas in the bubble is pushed outward to form a thin gas layer near the surface and the radial viscous fingering pattern is formed at the dielectric layer. We compare the thickness of the thin gas layer with the theoretical value according to Saffman-Taylor instability.