A Cu-containing Nb3Al multifilamentary superconductive wire having a multifilamentary (superfine multi-core) structure that a large number of micro-complex cores each obtained by complexing a Cu—Al alloy containing Cu in an amount of more than 0.2 at. % and at most 10 at. % in Nb are embedded in Nb, Ta, an Nb alloy or a Ta alloy as a matrix, wherein in the micro-complex cores, an A15 phase compound structure is formed by rapid heating at a temperature of 1,700° C. or more for 2 seconds or less and quenching to approximately room temperature, and further additionally heat-treated at a temperature of 650 to 900° C.