Nb₃Al multifilamentary wire made by a rapid heating, quenching and transforming (RHQT) process shows not only 3-5 times higher J_c (4.2K), but also much lower strain sensitivity of superconductivity than that of commercialized (Nb, Ti)₃Sn multifilamentary wire, and is therefore one of the most promising candidates as a next-generation superconductor. However, the Cu stabilization process is an unsolved key technology required to commercialize the RHQT-processed Nb₃Al conductor. Because the RHQT process includes heat treatment at about 2, 000°C, which is much higher than the melting point of pure Cu, we must cover the Nb₃Al wire with a Cu stabilizer after quenching. A stable Nb oxide layer is formed on the surface of the Nb₃Al wire and prevents electrical and thermal conductivities between the Cu stabilizer and Nb₃Al wire. We found that a 1μm thick Cu-ion plating on the Nb₃Al wire removes the Nb oxide layer effectively. The Nb₃Al wire, Cu-plated electrically with several tens of micrometers in thickness after being Cu-ion plated, shows improved J_c in lower fields and an increase in recovery current, which indicates the improved stability of the Nb₃Al wire.