A super-conducting magnet apparatus in an MRI system which may reduce unevenness among magnetization characteristics of ferromagnetic elements arranged between super-conductive shield coils and superconducting main coils. There are provided a pair of super-conducting main coils, a pair of superconductive shield coils arranged on the axes of the pair of super-conducting main coils, being spaced from the pair of super-conducting main coils, and also arranged on opposite sides of a zone to be observed, and ferromagnetic elements arranged in parts of spaces extending from air core parts of the super-conducting main coils to air core parts of the super-conductive shield coils. The super-conductive shield coils have an outer diameter which is larger than that of the super-conducting main coils. The ferromagnetic elements are composed of a plurality of axially symmetric ferromagnetic members which are coaxially arranged, and which have a space in at least a radial part thereof, but not in a center axis part. With this configuration, the magnetic saturation of the ferromagnetic members may be facilitated. Thereby it is possible to reduce the effect of unevenness among magnetization characteristics of the ferromagnetic elements.