Effects of Cu addition on the glass-forming ability (GFA), thermal stability, magnetic properties and crystallization process of (Fe0.76Si0.09B0.1P0.05)99−xNb1Cux (x = 0, 0.25, 0.5, 0.75, 1) alloys were investigated. The introduction of Cu effectively stimulates the precipitation of the α-Fe(Si) without obvious deterioration of the GFA, and successfully modifies the simultaneous precipitation of α-Fe(Si), Fe2B and Fe3(B,P) phases in (Fe0.76Si0.09B0.1P0.05)99Nb1 alloy into separable precipitation of each phase at different temperatures during annealing, leading to the enhancement of soft magnetic properties. The saturation magnetic flux density of the representative (Fe0.76Si0.09B0.1P0.05)98.25Nb1Cu0.75 alloy could be enhanced from 1.43 to 1.51 T after annealing at 530 °C for 10 min due to the precipitation of α-Fe(Si) nanoparticles with a diameter of about 22 nm dispersing randomly in the amorphous matrix. The integration of high GFA and excellent soft magnetic properties makes the FeSiBPNbCu alloys promising soft magnetic materials for industrial applications.