Abstract: As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel efficiency and robustness of the proposed method by applying it to million-cell benchmark problems.