A special version of multi-grid method for solving multidimensional (2D and 3D) boundary value problems is considered, on the basis of three embedded rectangular grids (coarse, moderate and fine) and fast incomplete factorization iterative algorithms with the conjugate gradient acceleration (IFCG). The idea is to construct the robust procedure which would provide a considerable speedup, as compared to the original efficient IFCG method, but not to investigate the asymptotically optimal order convergence, because involving the coarser grids can decrease the total CPU time by several percent only, but increases considerably the complexity of the algorithm. The discussed approach is, in a sense, an improvement of the proposed in [1] acyclic multi-grid method whose analog was later called a cascadic algorithm [2]. The extension of a coarse solution to a moderate mesh is made by application of the linear interpolation, solution of the reduced subsystem with the finite condition number and refinement on the basis of iterative defect correction technique. The computation of a fine solution is realized by means of the "internal grid" extrapolation approach (modification of Richardson's one) at the coarse nodes and implementation of a special block IFCG method for solving the reduced subsystem for unknowns at the rest fine nodes. The efficiency of the proposed three-level algorithm is demonstrated on various numerical examples. References [1] V.P.Il'in. One version of the multigrid method.- Siberian Math. J., 1985, vol. 26, N 2, p. 240-244. [2] P.Deuflhard. Cascadic conjugate gradient methods for elliptic partial differential equations I.Algorithm and numerical results.- Technical report SC 93-23, Konrad Zuse Zentrum, Berlin, 1993.