The effect of B2O3 fluxing on the glass-forming ability (GFA), the structure and the soft magnetic properties of Fe (-Co)-B-Si-Nb bulk metallic glasses (BMGs) has been investigated. The large Fe-Co-B-Si-Nb BMG specimens with diameters up to 7.7 mm, which is approximately 1.5 times as large as that of the maximum diameter of the copper mold cast one (= 5 mm), were prepared by the fluxing and water quenching. Thus the GFA of the Fe-Co-B-Si-Nb BMG are improved by the fluxing. It was confirmed that the soft magnetic properties of the Fe-Co-B-Si-Nb BMG are also improved by the fluxing. On the other hand, it was found for the Co-free Fe-B-Si-Nb BMG that the B2O3 fluxing promotes the precipitation of the α-Fe (-Si) and Fe2B phases in the central region of the specimens; i.e., the GFA of the Fe-B-Si-Nb BMG is decreased by the fluxing. The Fe-B-Si-Nb BMG specimens show a flat hysteresis loop, indicating a good linear relationship between the magnetic induction and the applied magnetic field. These results of the Fe-B-Si-Nb BMG show that it is possible to develop a new soft magnetic material that exhibits constant permeability, which is necessary for producing inductors and choke coils.