Aggregation of the amyloid-β (Aβ) protein and the formation of toxic aggregates are the possible pathogenic pathways in Alzheimer’s disease. Accumulating evidence suggests that lipid membranes play key roles in protein aggregation, although the intermolecular forces that drive the interactions between Aβ-(1–40) and the membranes vary in different membrane systems. Here, we observed that a high positive curvature of lipid vesicles with diameters of ∼30 nm enhanced the association of Aβ with anionic phosphatidylglycerol membranes in the liquid-crystalline phase and with zwitterionic phosphatidylcholine membranes in the gel phase. The binding modes of Aβ to these membranes differ in terms of the location of the protein on the membrane and of the protein secondary structure. The fibrillation of Aβ was accelerated in the presence of the vesicles and at high protein-to-lipid ratios. Under these conditions, the protein accumulated on the surfaces, as demonstrated by a high (10⁷ M^–1) binding constant. Our findings suggest that packing defects on membranes with high curvatures, such as the intraluminal vesicles in multivesicular bodies and the exosomes, might result in the accumulation of toxic protein aggregates.