As a result of the interplay between advances in computer hardware, software, and algorithms, we are now in a new era of large-scale simulation. Fine-scale reservoir simulations focus on fine reservoir characterization, accurate flow description, efficient nonlinear and linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in the new-generation simulator HiSim developed by RIPED, PetroChina. This preconditioner relies on the method of subspace corrections (MSC) to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. Unlike traditional purely algebraic methods, the proposed preconditioner takes into account some of the properties of pressure, saturation, and implicit well variables. We investigate the efficiency and robustness of the proposed method by applying it to a million-cell benchmark problems, and a real-world matured reservoir with high heterogeneity, high water-cut, geological faults, and complex well scheduling. The numerical results indicate that the proposed method is robust with respect to the heterogeneity, anisotropy, and number of wells.