Feasibility study of Cu stabilized Nb3Al strand and Rutherford cable for the application to high field accelerator magnets are being done at Fermilab in collaboration with NIMS. The Nb3Al strand, which was developed and manufactured at NIMS in Japan, has a non-copper Jc of about 844 A/mm2 at 15 Tesla at 4.2 K, a copper content of 50%, and filament size of about 50 microns. Rutherford cables with 27 Nb3Al strands of 1.03 mm diameter were fabricated and tested. Quench tests on a short cable were done to study its stability with only its self field, utilizing a high current transformer. A pair of 2 meter long Nb3Al cables was tested extensively at CERN at 4.3 and 1.9 K up to 11 Tesla including its self field with a high transport current of 20.2 kA. In the low field test we observed instability near splices and in the central region. This is related to the flux-jump like behavior, because of excessive amount of Nb in the Nb3Al strand. There is possibility that the Nb in Nb3Al can cause instability below 2 Tesla field regions. We need further investigation on this problem. Above 8 Tesla, we observed quenches near the critical surface at fast ramp rate from 1000 to 3000 A/sec, with quench velocity over 100 m/sec. A small racetrack magnet was made using a 14 m of Rutherford cable and successfully tested up to 21.8 kA, corresponding to 8.7 T.