The increase in Cu content from 1.0 to 1.7 at.% changes the as-spun Fe86-xSi2B8P4Cux and Fe84-yMn2Si2B8P4Cuy alloys from a single amorphous phase to a composite of -Fe nanoparticles dispersing in amorphous matrix and significantly refines the nanostructure and improves the magnetic softness of the annealed alloys. The as-spun Fe82.3Mn2Si2B8P4Cu1.7 amorphous alloy containing high number density -Fe nanoparticles forms uniform nanostructure with fine -Fe grains in an average size of 17nm after annealing and exhibits low coercivity of 8.4 Am-1 and high effective permeability of 15000 at 1kHz, which are superior to those of 38nm, 85.4 Am-1 and 1400, respectively, for the Fe83Mn2Si2B8P4Cu1 amorphous alloy. The mechanism relating to the effect of Cu content on the grain refinement was discussed in terms of the as-spun structure and crystallization process of the alloys.