The aggregation of human islet amyloid polypeptide (hIAPP) is linked to the death of pancreatic β-cells in type II diabetes. The process of fibril formation by hIAPP is thought to cause membrane damage, but the precise mechanisms are still unclear. Previously, we showed that the aggregation of hIAPP in the presence of membranes containing anionic lipids is dominated by secondary nucleation events, which occur at the interface between existing fibrils and the membrane surface. Here, we used vesicles with different lipid composition to explore the connection between hIAPP aggregation and vesicle leakage. We found that different anionic lipids promote hIAPP aggregation to the same extent, whereas remarkably stochastic behaviour is observed on purely zwitterionic membranes. Vesicle leakage induced by hIAPP consists of two distinct phases for any of the used membrane compositions: (i) an initial phase in which hIAPP binding causes a certain level of leakage that is strongly dependent on osmotic conditions, membrane composition and the used dye, and (ii) a main leakage event that we attribute to elongation of hIAPP fibrils, based on seeded experiments. Altogether, our results shed more light on the relationship between hIAPP fibril formation and membrane damage, and strongly suggest that oligomeric intermediates do not considerably contribute to vesicle leakage.