Although many composite structures are inconsistently curved, such as the leading edges of aircraft wings, the variety of research in impact engineering is almost limited to the impact performance of plates or cylindrically curved specimens. It is not known whether the findings obtained from standardized tests can be transferred to curved structures or which adaptions are required. Therefore, a deeper understanding of the deformation and damage behavior of inconsistently curved structures is essential to transfer the observed impact behavior of flat specimens to general curved structures and therefore to utilize the full lightweight potential of a load-specific design. An accurate description of the procedure as well as the results of the experimental and numerical study of the low-velocity impact behavior of differently single-curved elliptic specimens is presented. To close the research gap of the impact behavior of geometries with curvatures between the plates and simplified leading edges, novel specimens geometries have been derived from established impact test standards. Glassfiber-reinforced specimens are subjected to an instrumented impact test at constant impact energy. This is numerically investigated by a stacked-layer model, which used cohesive zone modeling to enable the simulation of matrix cracking, fiber fracture and delamination. The resulting projected damage areas, as well as the force and deflection histories, were evaluated and section cuts were examined to discuss the damage morphology, formation and propagation process. Significant effects on maximum deflection, compliance and dynamic behavior on the size and morphology of damage were found.