An oxide superconductor member is composed of a tape-shaped substrate, an intermediate layer formed on this substrate and an oxide superconductor thin film layer formed on this intermediate layer. A surface of the tape-shaped substrate is polished by continuously running the tape-shaped substrate. The polishing step includes initial polishing process and finishing process which are carried out such that the average surface roughness Ra of the substrate becomes 2 nanometers or less and the in-plane directionality of the intermediate layer becomes 5° or less after the polishing step.