It is well established that sedimentary basins can significantly amplify earthquake ground motion. However, the amplification at any given site can vary with earthquake location. To account for basin response in probabilistic seismic hazard analysis, therefore, we need to know the average amplification and intrinsic variability (standard deviation) at each site, given all earthquakes of concern in the region. Due to a dearth of empirical ground-motion observations, theoretical simulations constitute our best hope of addressing this issue. Here, 0–0.5 Hz finite-difference, finite-fault simulations are used to estimate the three-dimensional (3D) response of the Los Angeles basin to nine different earthquake scenarios. Amplification is quantified as the peak velocity obtained from the 3D simulation divided by that predicted using a regional one-dimensional (1D) crustal model. Average amplification factors are up to a factor of 4, with the values from individual scenarios typically differing by as much as a factor of 2.5. The average amplification correlates with basin depth, with values near unity at sites above sediments with thickness less than 2 km, and up to factors near 6 above the deepest (≈ 9 km) and steepest-dipping parts of the basin. There is also some indication that amplification factors are greater for events located farther from the basin edge. If the 3D amplification factors are divided by the 1D vertical SH-wave amplification below each site, they are lowered by up to a factor of 1.7. The duration of shaking in the 3D model is found to be longer, by up to more than 60 seconds, relative to the 1D basin response. The simulation of the 1994 Northridge earthquake reproduces recorded 0–0.5 Hz particle velocities relatively well, in particular at near-source stations. The synthetic and observed peak velocities agree within a factor of two and the log standard deviation of the residuals is 0.36. This is a reduction of 54% and 51% compared to the values obtained for the regional 1D model and a 1D model defined by the velocity and density profile below a site in the middle of the basin (DOW), respectively. This result suggests that long-period ground-motion estimation can be improved considerably by including the 3D basin structure. However, there are uncertainties concerning accuracy of the basin model, model resolution, the omission of material with shear velocities lower than 1 km/s, and the fact that only nine scenarios have been considered. Therefore, the amplification factors reported here should be used with caution until they can be further tested against observations. However, the results do serve as a guide to what should be expected, particularly with respect to increased amplification factors at sites located above the deeper parts of the basin.