A simulated vortex within a large-eddy simulation is subjected to various surface terrain, implemented through the immersed boundary method, to analyze the effects of complex topography on vortex behavior. Thirty simulations, including a control with zero-height terrain, are grouped into four categories—2D sinusoidal hills, 3D hills, valleys, and ridges—with slight modifications within each category. A medium-swirl-ratio vortex is translated over shallow terrain, which is modest in size relative to the vortex core diameter and with no explicitly defined surface roughness. While domain size restricts results to the very near-field effects of terrain, vortex–terrain interaction yields notable results. Terrain influences act to increase the variability of the near-surface vortex, including a notable leftward (rightward) deflection, acceleration (deceleration), and an expansion (a contraction) of the vortex as it ascends (descends) the terrain owing to changes in the corner flow swirl ratio. Additionally, 10-m track analyses show stronger horizontal wind speeds are found 1) on upslope terrain, resulting from transient subvortices that are more intense compared to the control simulation, and 2) in between adjacent hills simultaneous with strong pressure perturbations that descend from aloft. Composite statistics confirm that the region in between adjacent hills has the strongest horizontal wind speeds, while upward motions are more intense during ascent. Overall, valley (ridge) simulations have the largest horizontal (vertically upward) wind speeds. Last, horizontal and vertical wind speeds are shown to be affected by other terrain properties such as slope steepness and two-dimensionality of the terrain.