A variable-grid finite-difference (FD) scheme is introduced for efficiently modeling viscoelastic wave propagation in 3D basins. The basin model includes a near-surface unconsolidated layer that is modeled with a fine grid and a deep part that is modeled by a coarse grid. The FD method changes the grid spacing in all three dimensions at a certain depth to provide a significant reduction in computational cost. It is an improvement on other variable-grid FD methods in that it can accommodate both 2× and 3× grid-spacing changes and a possible instability problem is overcome by a 3D interpolation scheme in the wavenumber domain. As an example, the variable-grid method is used to simulate the 3D viscoelastic response of a Salt Lake basin model. Simulation results show that the 3D basin features and the shallow layer significantly affect the amplitude and duration time of the ground motion. A basin model without a shallow low-velocity layer underestimates the ground-motion duration and cumulative kinetic energy by 50% or more. In this case, the variable-grid method requires 5 times less CPU time (and physical memory) compared to a standard FD method.