The structural stability of FePt nanoparticles of about 5-6nm diameter was investigated by dynamic high resolution transmission electron microscopy. The FePt icosahedra were very stable under an electron beam flux of～20 A/cm2 at 300 kV. Surface sputtering was suppressed due to the large sputtering threshold energy of a Pt-rich shell. Under a flux of～50 A/cm2, the trapping potential well of the FePt particle on the supporting carbon film was lowered by the magnetic interaction between the electron beam and the particle, which leads to rotational and translational motions of the particle. A large dose of electrons (of～200 A/cm2) initiated melting and recrystallization of the FePt particle. The structure of the FePt nanoparticle, a Pt enriched shell around an Fe/Pt magnetic core, is believed to be responsible for its dynamic behaviour under different beam conditions.