Focal position control of vortex beams has tremendous applications in optical field. Herein, non-classical Archimedean arrays were proposed for optical devices with bifocal length and polarization-switchable focal length. The Archimedean arrays were constructed by rotational elliptical holes in a silver film, which were followed by two one-turned Archimedean trajectories. The elliptical holes in this Archimedean array provide the freedom of polarization control for the optical performance by their rotation status. The rotation of elliptical hole can provide additional phase to affect the shape of vortex beam (converged or diverged) under the illumination of circular polarization. The geometric phase of Archimedes trajectory will also determine the focal position of vortex beam. This Archimedean array can produce a converged vortex beam at the specific focal plane according to the handedness of the incident circular polarization and geometrical arrangement of array. The Archimedean array was also demonstrated by experiment and numerical simulation for its exotic optical performance.