In order to clarify the dominant factors for excellent soft magnetic properties of nanocrystalline bcc Fe-Zr-B alloys, we examined the change in the microstructure, soft magnetic properties and magnetostriction (λs) of an Fe86Zr7B6Cu1 amorphous alloy upon crystallization. The amorphous phase changed to a mostly single bcc phase with a grain size of about 10 nm by annealing for 3.6 ks at temperatures between 773 and 923 K. The phase transition causes a marked reduction of λs from 16.6 × 10-6 to an extremely low value of 10-7. The permeability (μc) also increased significantly by the transition to the nanocrystalline bcc phase and reached a maximum value of 48000 at Ta=873 K at which the λs approaches zero value. Thus, the excellent soft magnetic properties seem to result from the simultaneous satisfaction of small λs and nanocrystalline bcc structure. Consequently, it appears important for the achievement of the good soft magnetic properties that the nanocrystalline structure remains almost unchanged up to the high temperature range where the nearly zero λs value is obtained. Based on the data for the temperature dependence of magnetization and μe, it is presumed that the high thermal stability of the nanocrystalline bcc phase is due to the presence of an amorphous thin layer with higher Zr and B contents along the grain boundary of the bcc phase.