We have conducted a comprehensive study on the magnetic properties of:five heavy rare-earth metallofullerenes M@C-82 (M = Gd, Tb, Dy, Ho, Er) in the temperature range of 1.8 and 300 K at a magnetic field up to 5 T. The isothermal magnetization curves of the endohedral metallofullerenes follow the Brillouin function only above certain temperatures. The fittings to the Curie-Wiess law and to the Brillouin function for the heavy rare-earth metallofullerenes both result in effective magnetic moments that are significantly smaller than those of the corresponding free M3+ ions. The magnetic moment reduction and the imperfect paramagnetic behavior of M@C-82 were found to be related to the orbital angular momentum of entrapped M3+ ions. The fullerene cage crystal field splitting, the partial hybridization of the orbitals of the entrapped metal atom and the carbon cage, and the interactions between the metal centers were proposed to account for the peculiar magnetic behaviors of the endohedral metallofullerenes.