A general method of the asymptotic expansion for elastic hadron-hadron diffraction scattering amplitudes is presented in the impact-parameter representation. The asymptotic series for the scattering amplitude is given in terms of the black-disk amplitude and its successive derivatives with respect to the black-disk radius by assuming only physically reasonable behavior for the eikonal. The asymptotic amplitude consists of two components, the black disk and the peripheral ring, and shows a similarity to the Regge-type amplitude of Gauron, Nicolescu and Leader based on the complex-angular-momentum-plane singularity.