With the development of electromagnetic devices towards high-frequency, miniaturization, and high efficiency, the demand for the soft magnetic nanocrystalline alloys with high saturation magnetic flux density (B_s), excellent high-frequency performance, as well as good manufacturability is becoming increasingly urgent. In this work, the effects of B content on the melt-spun structure, thermal stability, crystallization structure, and magnetic properties of Fe_{98.5 - x} B _x Cu_1.5 (x = 12-18, atomic fraction, %) alloy ribbons were investigated; and the correlation among B content, melt-spun structure, crystallization structure, and magnetic properties was explored. The results show that the melt-spun structure of all the alloys is a dual-phase composed of α-Fe nanograins distributing in an amorphous matrix. As the x increases from 12 to 18, the number density and grain size of the α-Fe grains gradually decrease, and the structure transforms into a nearly amorphous state. After crystallization annealing under a low heating rate, the alloys with x = 12-17 have the amorphous/nanocrystalline α-Fe dual-phase structure, while the x = 18 alloy forms a amorphous/α-Fe/Fe₃B tri-phase structure. The alloys with x = 13-16 exhibit a fine nanocrystalline structure and good soft magnetic properties with the average α-Fe grain size (\overline{D}_α-Fe) of 15.8-16.3 nm, B_s of 1.80-1.91 T, and coercivity (H_c)of 18.9-22.7 A/m. Among them, the alloywith x = 15 has the \overline{D}_α-Fe, B_s, and H_c of 16.0 nm, 1.86 T, and 18.9 A/m, respectively. Based on the structure of the alloys before and after annealing, a crystallization model for the melt-spun alloys with different B contents was proposed, and the mechanism of which the strong competitive growth effect between the high-number-density pre-existing fine α-Fe nanograins in the amorphous matrix of the melt-spun alloys along with the newly-formed α-Fe grains during crystallization annealing results in the uniform and fine nanocrystalline structure of the alloys was elucidated.