In this study, we calculated the diffusion of an Fe atom on graphene and various light-element (B, N, O, Si, P, and S)-doped graphene supports, using first-principles calculations based on density functional theory. We focused on dopants that could suppress the detachment and diffusion of an Fe atom. Such doped graphene supports would have strong potential in high-durability fuel cell catalysts and hydrogen storage materials. The Fe atom adsorbs on pristine graphene via ionic bonding. The bonding between the Fe atom and pristine graphene is very weak, and it has a low adsorption energy of −0.61 eV. Doped graphene contains unoccupied localized orbitals. B-, O-, Si-, and P-doped graphene show high adsorption energies of −1.70 eV, −2.70 eV, −1.46 eV, and −1.38 eV, respectively. Thus, these graphene supports could suppress the detachment of Fe nanoclusters and nanoparticles. We demonstrate that these doped graphene supports with high adsorption energies also have high diffusion barriers, which suppresses the agglomeration of Fe nanoclusters and nanoparticles. We conclude that B-, O-, Si-, and Pdoped graphene are promising supports for enhancing the adsorption lifetime of Fe nanoclusters and nanoparticles.