Carbon fiber reinforced polymer (CFRP) composites are widely used in curved aerospace structures, where riveting-induced interlaminar damage is a critical concern. Existing studies have mainly focused on flat laminates, while the influence of structural curvature on rivet load transfer and delamination tendency remains insufficiently understood. In this study, a three-dimensional nonlinear finite element model was developed in ANSYS Workbench to investigate the curvature–interference coupling effect in CFRP/Al single-lap riveted joints. Four curvature configurations with identical arc length but different bending angles (C0, C45, C90, and C180) were established. The riveting process was simulated using a quasi-static displacement-controlled method with rivet upsetting displacements of 1.5–3.0 mm.The results show that curvature alters the load-transfer mechanism around the rivet hole. The contact pressure distribution evolves from an approximately axisymmetric pattern in the flat laminate to a strongly localised distribution on the convex side of curved laminates. Meanwhile, the deformation mode changes from nearly isotropic radial expansion to hoop-dominated deformation. With increasing curvature and upsetting displacement, the equivalent interlaminar shear stress increases nonlinearly. At a rivet upsetting displacement of 3.0 mm, the peak stress in the C180 configuration reaches 415.9 MPa, 1.86 times that of the flat laminate. Further analysis indicates that curvature induces membrane–bending coupling, which amplifies deformation incompatibility between adjacent plies and increases interlaminar delamination tendency. The findings indicate that riveting parameters developed for flat laminates may not be directly applicable to curved composite structures and that curvature effects should be considered in the damage-tolerant design of aerospace composite joints.