Utilizing first-principle calculations, the structural, electronic and magnetic properties of monolayer graphene embedded with Fe-n/X-m (X=C,N,O,Cl,S and F) core/shell clusters are investigated, where n=1, 2, 3 and m=4, 6, respectively. We find that the graphene embedding with the Fen/Xm core/shell clusters are magnetic except the Fe/S-4, Fe-2/C-4 and Fe-3/CI6 core/shell clusters. The graphene embedding with the Fe-3/F-6 core/shell cluster has the largest magnetic moment in these systems. Magnetism for Fen/Xm core/shell clusters embedded in monolayer graphene can be ascribed to the ferromagnetic coupling between the Fe atoms. Our calculations demonstrate that Fe atoms are successfully isolated at various C,N,O,Cl, S and F shells in graphene to preserve the high-spin state. On the other hand, the high-spin state is also effectively controlled by the amount of Fe atoms. The electron spin can be stored in magnetic thin film, lithographically prepared quantum dots, and electromagnetic traps. The Fen/Xm core/shell clusters embedded in graphene can be considered to have potential applications in nanoelectronics, spintronics and magnetic storage devices. (C) 2016 Elsevier B.V. All rights reserved.