We propose a new, efficient, adaptive algebraic multigrid (AMG) solver strategy for the discrete systems of partial-differential equations (PDEs) arising from structured or unstructured grid models in reservoir simulation. The proposed strategy has been particularly tailored to linear systems of equations arising in adaptive implicit methods (AIMs). The coarsening process of the AMG method designed automatically employs information on the physical structure of the models; as a smoother, an adaptive incomplete LU factorization with thresholding (ILUT) method is employed, taking care of an efficient solution of the hyperbolic parts while providing adequately smooth errors for the elliptic parts. To achieve a good compromise of high efficiency and robustness for a variety of problem classes—ranging from simple, small black-oil to challenging, large compositional models—an automatic, adaptive ILUT parameter and AMG solver switching strategy, α-SAMG. has been developed. Its efficiency is demonstrated for eight industrial benchmark cases by comparison against standard one-level and AMG solvers, including constraint pressure residual (CPR), as well as the pure one-level variant of the proposed new strategy. In addition, very promising results of first parallel runs are shown.