When seismic waves encounter abrupt points of stratum or lithology in the process of propagation, such as fault edges, pinch out points of stratum and the protrusion of unconformity surfaces, the Snell law will break down and many diffractions will be generated. Therefore, diffractions on seismic profile can be used to identify discontinuous geological structures. However, the diffraction information is typically masked by strong reflections, thus separating diffractions is one key issue for diffraction imaging. The traditional SVD (Singular Value Decomposition) method with the ability for wave-field decomposition and reconstruction, has a potential in removing strong reflections with large singular values. However, the continuously changing characteristics of singular value of steep-slope reflections make it difficult to optimally choose a suitable parameters for separating diffractions. To solve the problem of singular value selection in diffractions reconstruction by SVD method, we propose a Cook-distance SVD method by mathematically least-square measuring the contribution of every singular value. The Cook-distance SVD can amplify the difference between continuously changing singular values and easily find the singular values representing diffractions. Synthetic example and field data applications demonstrate that the proposed Cook-distance SVD method can avoid parameter testing and has good performance in diffraction separation, and can highlight reservoir-involved small-scale geological edges and scatterers.