A method of fabricating a superconductive electrical conductor of Nb.sub.3 Sn type comprises a step of covering an elongated core member made of Nb with a covering member made of a third element selected from the group consisting of Ti, Ta, In, Hf, Al and Si. The core member covered with the covering member is covered with a tubular matrix made of a Cu-Sn alloy or a combination of Cu with Sn to form a composite wire element. Such wire elements are assembled in a tubular matrix made of a Cu-Sn alloy, Cu or a combination of Cu with Sn and reduced in diameter to form a multi-core composite wire element having a desired diameter. The assembling and reducing processing is effected at least one to form a multi-core composite wire which is then subjected to a diffusion heat-treatment to form an intermetallic compound of Nb.sub.3 Sn and the third element in the peripheral portion of the core member.