Fe-based amorphous alloys are well known for their good magnetic properties including ultrahigh saturation magnetization, low coercive force, high magnetic permeability and low core loss. But these alloys were only prepared into ribbon form in early times due to their insufficient glass-forming abilities (GFAs). The present work focuses on the design of Fe-B-Si-Nb bulk metallic glasses with good soft magnetic properties and high glass-forming ability. Glass formation in Fe-B system is first considered with cluster-plus-glue-atom model. A basic composition formula [B-B₂Fe₈]Fe is proposed as the framework for multi-component alloy design. Considering the structural stability of the model glass, Si and Nb are introduced to the [B-B₂Fe₈] cluster to replace the center B and shell Fe atoms, from which a series of Fe-B-Si-Nb alloys with composition formulas [Si-B₂Fe_8-xNb_x]Fe (x=0.1~1.2) are derived. Copper mold casting experiments revealed that bulk glass alloys with a critical diameter (d_c) exceeding 1.0 mm are readily obtained with the Nb content range of x=0.2~1.2, the largest d_c (about 2.5 mm) appears in the vicinity of x=0.4~0.5. Considering the local packing efficiency of Fe-B-Si-Nb glass model structure, another series alloy compositions, namely, [(Si_1-yB_y)-B₂Fe_8-xNb_x]Fe is reached by increasing Nb and decreasing Si simultaneously in [Si-B₂Fe_7.6Nb_0.4]Fe basal glass alloys. The experimental results show that bulk glass alloys with d_c=2.5 mm are available over a wide range of compositions from (x=0.5, y=0.05) to (x=0.9, y=0.25). Excellent magnetic softness with high saturation magnetizations (B_s=1.14~1.46 T) and low coercive forces (H_c=1.6~6.7 A/m) is found in the [Si-B₂Fe_8-xNb_x]Fe (x=0.2~0.6) series glass alloys. A high fracture strength of 4220 MPa with a plasticity of 0.5% is observed in the [(Si_0.95B_0.05)-B₂Fe_7.5Nb_0.5]Fe bulk glass alloy.