To promote energy savings, high efficiency and miniaturization of power electronic devices, Fe–Si–B–P–Cu nanocrystalline soft magnetic materials with high saturation magnetization (Bs) parallel to that of the 6.5 wt% Si steel and low coercivity (Hc) are desired. In this work, 30 μm-thick Fe84Si3B10P2Cu1 and Fe84.5Si3B9.5P2Cu1 (at.%) amorphous/nanocrystalline precursor ribbons were melt-spun, which has high Fe contents comparable to that of the 6.5 wt% Si steel. These ribbons consist of an amorphous matrix and pre-existing α-Fe of approximately 28–30 nm in size possessed relatively low and similar-value activation energy of nucleation and growth in the range of 224–249 kJ/mol. Which could induce strong crystallization competition and effectively suppress coarsening of the pre-existing α-Fe. The Fe84Si3B10P2Cu1 nanocrystalline alloy obtained by rapid-annealing (∼100 °C/s) the amorphous/nanocrystalline precursor at 480 °C for 30 s (Fe84-480) exhibited a fine and uniform nanostructure containing α-Fe with small average grain size of approximately 23.1 nm and high volume fraction. The Fe84-480 alloy possessed a high Bs of approximately 1.88 T, a low Hc of 8.6 A/m, and good bendability revealed by relatively large bending fracture strain of ∼1.65%, making it a promising soft magnetic material for power electronic devices.