Quasicrystal hole arrays are expected to be adopted as new focusing optical elements, owing to the characteristic self-imaging effect and the possibility of overcoming the diffraction limit. Using one such element, we achieved soft X-ray focusing. We designed a fivefold symmetric quasicrystal based on a Penrose tiling pattern consisting of 301 1.5 μm diameter holes. The light source was 10 nm synchrotron radiation. The observed diffraction pattern agreed well with the results of Fraunhofer-approximation simulations. Furthermore, the focal spot size was estimated by direct CCD imaging and found to be sufficiently small, in line with simulation results.