Nanoperm-type alloy ribbons suffer from surface crystallization during melt spinning, which degrades their magnetic properties after annealing and limits their commercial application. Here, we investigate the effects of Cu addition on the structure and magnetic properties of a surface-textured Fe87-xHf5B8Cux alloy. Adding Cu (1 ≤ x ≤ 2) removes the surface coarse grains in the free surface of the melt-spun precursor, while induces the precipitation of large amounts of the α-Fe nanoparticles with ∼3 nm in size, which contributes a homogeneous ultrafine structure and improved magnetic softness after annealing. The grain size, coercivity, saturation magnetic flux density, and effective permeability at 1 kHz of the Fe86Hf5B8Cu1 nanocrystalline alloy are 13.3 nm, 6.6 A/m, 1.68 T, and 23000, respectively, whereas these are 16.0 nm, 16.8 A/m, 1.70 T, and 15000, respectively, for the Fe87Hf5B8 alloy. The Cu-improved effect is mainly attributed that Cu induces heterogeneous nucleation of the α-Fe phase to strengthen the competitive growth among grains.