To obtain accurate independent-particle descriptions for ferromagnetic two-dimensional van der Waals materials, we apply the quasiparticle self-consistent GW (QSGW) method to VI3, CrI3, CrGeTe3, and Fe3GeTe2. QSGW provides a description of the nonlocal exchange-correlation term in the one-particle Hamiltonian. The nonlocal term is important not only as the U of density functional theory (DFT) + U but also for differentiating occupied and unoccupied states in semiconductors. We show the limitations of DFT + U in mimicking QSGW.