The nanocrystalline-forming element Cu and magnetic element Co are commonly used as additive elements to tune the structure and improve properties of alloys. In this study, four kinds of amorphous alloys, Fe72Nb12B16, Fe72Nb12B15Cu1, Fe36Co36Nb12B16, and Fe36Co36Nb12B15Cu1, were prepared by melt-spinning and annealed at various temperatures to investigate the effects of Cu and Co additions, individually and in combination, on the crystallization and magnetic properties of Fe72Nb12B16 alloy. The four kinds of alloys exhibited different crystallization behaviors with different primary crystallization phases observed. For the Fe72Nb12B16alloy, only the α-Mn-type metastable phase formed after annealing. The addition of 1 at.% Cu and 36 at.% Co led to the observation of the α-Mn-type and β-Mn-type metastable phases, respectively, and a reduction in the crystallization volume fraction in the metastable phase. The Fe36Co36Nb12B15Cu1alloy only exhibited α-Fe(Co) phase as a primary phase, and the addition of both Cu and Co completely inhibited the precipitation of the metastable phase. Cu clusters were found in energy dispersive spectroscopy elemental maps. Compared with other alloys, Fe36Co36Nb12B15Cu1 alloy with both Cu and Co exhibited a lower coercivity (Hc) below 973 K.