This study deals with the complexity of creeping discharge patterns on water solution depending on conductivity ranging from 0.1 to 50 mS/cm. The same voltage peak of 20 kV was applied to needle electrode placed above the water solution at each conductivity of water. The pulse width of voltage decreased concomitantly with discharge current increased with increasing conductivity of water. A box counting method commonly-used as fractal analysis was adopted to estimate the fractal dimension of creeping discharge patterns on water. The fractal dimension of discharge patterns increased with increasing the water conductivity although propagation length of the creeping discharge decreased with increasing the water conductivity. The fractal dimension versus conductivity of water characteristic may be due to the discharge current and the pulse width of voltage.