In this paper, we study the strong Levitin-Polyak well-posedness for a class of generalized quasi-variational inclusion problems. We establish some metric characterizations of the strong Levitin-Polyak well-posedness for the generalized quasi-variational inclusion problem. We also prove that under suitable conditions, the strong Levitin-Polyak well-posedness of the generalized quasi-variational inclusion problem is equivalent to the existence and uniqueness of solutions, and that the strong Levitin-Polyak well-posedness of generalized quasi-variational inclusion problem in the generalized sense is equivalent to the existence of solutions. As applications, we obtain some results concerned with Levitin-Polyak well-posedness for several kinds of equilibrium problems.