In this work, Fe80-xMxP13C7 (M = Co, Ni; x = 0, 5 and 10 at.%) bulk metallic glasses (BMGs) were prepared, and the effect of the Co/Ni elements substitution for Fe on the magnetocaloric properties of Fe80P13C7 BMG has been investigated systematically. The Curie temperature (TC) of the present Fe-based BMGs increases with the substitution of Fe by Co/Ni. The magnetic entropy change (ΔSM) of the present Fe-based BMGs increases first and then decreases with the increase of Fe substituted by Co, but monotonically decreases with the increase of Fe substituted by Ni. Among the present Fe-based BMGs, the Fe75Co5P13C7 BMG exhibits the maximum ΔSM value of 5.21 J kg−1 K−1 at an applied field of 5 T, which is the largest value among Fe-based amorphous alloys without any rare earth elements reported so far. The present Fe-based BMGs exhibit the large glass forming ability, tunable TC and enhanced ΔSM value, which are beneficial for magnetic refrigerant materials.