In this paper a theoretical investigation has been made on the scattering of neutrons by the spin-wave in ferromagnetics with imperfections. The differential cross section of inelastic scattering has been calculated for a simple case. It has been found that the experimentation on scattering of thermal neutrons offers a method for the observation of localized modes of the spin-waves. In our calculation we have shown that the wave-functions of the scattered spin-waves and those of the localized modes form a complete set of orthonormalized wave-functions in the subspace in which the total deviation of spins is equal to unity.