Since Nb3Al shows better strain-tolerances of superconducting properties than those of Nb3Sn, the Nb3Al multifilamentary wire is one of the most promising candidate superconductors for the large-scaled high-field superconducting applications. Although the Nb3Al conductors with off-stoichiometric compositions fabricated by low-temperature diffusion reaction show higher J(c) values in fields below 14 T, their J(c) values rapidly decrease in high fields above 14 T due to their relatively low H-c2 (4.2 K) caused by their off-stoichiometric compositions. On the other hand the Nb3Al fabricated at high temperatures has a stoichiometric composition and improved H-c2 but shows relatively low J(c). Recently, we developed a new fabrication process of Nb3Al multifilamentary wire, in which Nb/Al-5 at%Mg multifilamentary composite wires were rapidly heated up to 2300 K and rapidly quenched to obtain composite wires including many Nb-Al supersaturated bcc filaments. Then, the resulting composites were annealed to form Nb3Al filaments through the deposition from the metastable Nb-Al bcc filaments. When the Al-5 at%Mg alloy core diameters were about 0.56 mu m, the wire showed the highest T-c and the highest J(c) (20 T, 4.2 K) of 17.4 K and 2.5 x 10(8) A/m(2), respectively. The optimized J(c) values are 2 similar to 3 times higher than those of the commercially available (Nb, Ti)(3)Sn multifilamentary wires. Small mechanical deformation (bending, twisting, and stranding) of the as-quenched composite wires did not degrade the superconducting properties of the final Nb3Al multifilamentary wires, which proves the good ductility of the supersaturated bcc filaments. Reducing temperature from 4.2 to 2.1 K shifted the J(c)-B curves to the higher magnetic field by 2.1 similar to 2.5 T and increased the n-index in the voltage-current characteristics from 14.3 to 31.7 at 20 T. All the test results indicate that the new wire is one of the most promising materials having a hopeful future in the various practical superconducting applications in high fields.