Fault roughness influences earthquake rupture dynamics, seismic energy radiation, and, hence, resulting ground motion and its variability. Using 3D dynamic rupture simulations considering a range of rough-fault realizations, we investigate the effects of rupture complexity caused by fault roughness on ground-motion variability, that is, the variability of peak ground acceleration (PGA) and velocity (PGV) as a function of distance. In our analysis, we vary hypocenter locations (leading to unilateral and bilateral ruptures) and fault roughness amplitude to generate a set of magnitude M ≈ 7 strike-slip dynamic rupture simulations. Synthetic seismic waveforms computed on a dense set of surface sites (maximum resolved frequency 5.75 Hz) form our database for detailed statistical analyses. For unilateral ruptures, our simulations reveal that ground-shaking variability (in terms of PGA and PGV) remains nearly constant with increasing distance from the fault. In contrast, bilateral ruptures lead to slowly decreasing ground-motion variability with increasing distance in the near field (less than 20 km). The variability becomes almost constant at large fault distances. We also find that low-amplitude fault roughness leads to ruptures that are likely to generate higher PGA variability than events on faults with high-amplitude roughness. Increasing fault roughness distorts the radiation pattern, thereby reducing directivity effects and, hence, potentially lowering ground-motion variability. The average PGV variability from our rough-fault rupture models is consistent with estimates from empirical ground-motion models (GMMs). However, the average PGA variability exceeds the variability encoded in empirical GMMs by nearly 20%. Hence, our findings have implications for near-source ground-motion prediction in seismic hazard studies, because groundmotion variability depends on details of the earthquake rupture process and is larger than GMM estimates.