A Josephson junction element having a substrate of a single crystal having a V-shaped notch formed in a surface of the substrate and a wiring pattern of an oxide superconductor formed on the surface of the substrate and crossing the notch to form a weak link region in the pattern at a position above the notch. The notch is defined by first and second walls joining with each other at the bottom of the notch and has first and second corners at which the first and second walls meet the surface of the substrate. The first and second corners have radii of curvature of 5-50 nm and 50-500 nm, respectively, provided that the difference in radius of curvature between the first and second corners is not smaller than 10 nm. The notch is formed by obliquely irradiating a predetermined portion of the substrate with a focused ion beam.