In this paper, calculation has been carried out for the localized modes of spin waves around a magnetic impurity atom in a ferromagnetic of the simple cubic structure. There are three symmetry types, i.e., the s-type, the p-type and the dr-type mode. The wave functions and the curves of the energy levels against the parameter J′S′/JS of these modes are obtained. Next, the types of localized modes which may possibly exist in ferromagnetics of the bcc or the fcc structure are discussed. It is pointed out that probably the s-type mode is the only one to be expected in actual specimens. With the criterion that the Curie point of the specimen should increase with the concentration of impurity, several alloys are suggested for the experimental observation of the localized modes of spin waves. Finally, a general analysis of the spin quantum number of the spin wave states leads to the conclusion that it is impossible to excite the scattered modes with k0≠0 as well as the localized modes by the electromagnetic radiation.