By applying an optimization method to supercavitating foil section design, the authors developed a new method to design super cavitating foil section automatically. Using this method, we designed 150 foils as a series foil sections. Then polynomial expressions were obtained by a method of least-squares for foil shapes and foil performance such as lift/drag ratio. By using these polynomials, one can obtain foil shape and estimate hydrodynamic performance for a set of a few design parameters including design lift coefficient and strength requirement. A trans-cavitating propeller (which adopted supercavitating-blade sections near the tip and noncavitating ones near the root) was designed using these series foil sections, and has realized high performance.