Solving the algebraic linear systems proceeding from the discretization on some condensed meshes of 2D singularly perturbed problems, is a difficult task. In this work we present numerical experiments obtained with the multigrid method for this class of linear systems. On Shishkin meshes, the classical multigrid algorithm is not convergent. We see that modifying only the restrict on operator in an appropriate form, the algorithm is convergent, the CPU time ncreases linearly with the discretization parameter and the number of cycles is independent of the mesh sizes.