Taking account of spin-multiplicity states，the ground-state structures of FeBN(N≤6)clusters have been predicted using the generalized gradient approximation(GGA) density functional theory. The results indicate that the spin-multiplicity states of the ground-state clusters are respectively 4,3,2,1,2 and 1，and FeB4 is the most stable of the clusters. Also, we studied magnetic properties of the ground-state clusters systematically and found that the magnetic moment of Fe atom and total magnetic moment are decreasing with the increasing of cluster size except FeB5.