The adsorption and dissociation of nitrogen molecule on Fe(111) surface is studied by density functional theory calculations. The simulation results show that the molecule needs to acquire parallel orientation with respect to the surface for the adsorption and dissociation. In addition, Fe(111) surface is more active in dissociating N2 than Fe(100) surface due to its morphology. The interaction between antibonding molecular orbitals of N2 and partially filled $3d$ orbitals of Fe atoms on the surface may be the key to the molecular dissociation of N2. To break down the triple bond of N2, the electron density on the surface needs to be partially transferred to the molecule to fill the antibonding molecular orbitals of the nitrogen molecule. The present result may provide some insights on the dissociation mechanism of molecules over transition metal surfaces.