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In collaboration between NIMS and Fermilab, we have made copper stabilized Nb3Al Rutherford cables, using Nb-matrixed and Ta-matrixed strands. First these cables were investigated at high current in low self field using a flux pump. Using these Rutherford cables, we built and tested small racetrack magnets. The magnet made with the Nb-matrixed strand showed the flux jump instability in low field. The small racetrack magnet wound with the Ta-matrixed Nb3Al Rutherford cable was very stable at 4.5 K operation without any instability, as well as at 2.2 K operation. With the successful operation of the small racetrack magnet up to its short sample data, the feasibility of the Nb3Al strand and its Rutherford cable for their application to high field magnets is established. The characteristics of Nb3Al Rutherford cable is compared with that of the Nb3Sn Rutherford cable and the advantages of Nb3Al Rutherford cable are discussed.