Liquid and amorphous Fe nanoparticles have been studied in spherical models with sizes of 3, 4 and 5 nm. We use the molecular dynamics (MD) method with the Pak-Doyam interatomic pair potential. Structural properties of Fe nanoparticles have been studied via radial distribution function (RDF), interatomic distances, coordination number distribution and radial density profile. Local icosahedral order was detected via using Honeycutt-Andersen (HA) analysis compared with that observed in the bulk counterparts. Surface and core structures of Fe nanoparticles have been studied in detail. Potential and surface energies of liquid and amorphous Fe nanoparticles have been calculated and discussed in addition to the size dependence of a glass transition temperature.