The effect of Si/Fe ratio on glass-forming ability, crystallization behavior, formed phase, and soft magnetic properties of Fe74-xSixBCuNbNiCo (X = 3, 4, 5, and 6) alloy ribbons is investigated. With decreasing the ratio of Si/Fe, the glass-forming abilities of Fe74-xSixBCuNbNiCo alloys decrease, the as-quenched X = 6 and 5 alloy ribbons are amorphous state, the X = 4 and 3 alloy samples precipitate FeNi3 in the amorphous precursors during melt-spinning technique. The as-quenched Fe74-xSixBCuNbNiCo (X = 3, 4, 5, and 6) alloy ribbons show two-stage crystallization behaviors; with X reducing, the onset temperature of the first crystallization decreases from 442 to 402 degrees C, and the temperature interval of onset crystallization of alpha-Fe and boride phases is 121-147 degrees C. After annealing at appropriate temperatures, with decreasing Si/Fe, the annealed Fe74-xSixBCuNbNiCo alloy samples show a significant decrease in Br and mu, which make the linearity of B-H hysteresis loop more pronounced. By comparison with X = 6 alloy, the annealed X = 3 alloy sample annealed at 480 degrees C x 60 min shows a great B-H linearity with a constant mu of 2.3k and higher Ms of 181 emu/g (Bs approximate to 1.7 T), leading to good resistance to DC bias in current transformers. The iron core with low mu and high Bs can enable current transformers to be used at high current power without saturation failure. Finally, we discussed that a high Bs and low constant mu in annealed X = 3 alloy could attribute to the coupling effect between alpha-Fe and FeNi3 nanocrystalline phases.