The effective magnetic anisotropy (Keff) of nanocrystalline Fe89Zr7B4soft magnetic alloys with different bcc Fe grain sizes (D) has been investigated by using the law of approach to saturation. The effective magnetic anisotropy of the alloys is found to be considerably depressed. The values ofKefffor the alloys (from 879 to 1038 J/m3) are very close to those of the nanocrystalline Fe73.5Cu1Nb3Si13.5B9soft magnetic alloys, suggesting that the relatively lower permeability of the alloys is independent of the factor ofKeff. With an increase of grain size,Keffis slightly increased. However, the grain size dependence ofKeffis obviously deviated from theKeff∝D6law, which might be mainly attributed to the residual amorphous phase in the alloys. ©1996 American Institute of Physics.