The paper combines the local defect-correction technique and multigrid discretization schemes to establish a new three-scale finite element scheme for a class of singular eigenvalue problems and their parallel versions. With these schemes, that are based on globally and locally coupled discretizations, the solution of an eigenvalue problen on a fine grid \(\pi _{h}\) is reduced to the solution of an eigenvalue problem on a coarser grid \( \pi _{H}\), the solution of a linear algebraic system on a globally mesoscopic grid \(\pi _{w}\) and the solutions of linear systems on several locally fine grids in parallel. The principle to determine the diameters of the three different scale grids is given and error estimates are calculated.