Human islet amyloid polypeptide (IAPP) forms amyloid fibrils in the pancreatic islets of patients suffering from type 2 diabetes mellitus (T2DM). The formation of IAPP fibrils has been shown to cause membrane damage which most likely is responsible for the death of pancreatic islet β-cells during the pathogenesis of T2DM. Several studies have demonstrated a clear interaction between IAPP and lipid membranes. However the effect of different lipid compositions and of various membrane mimetics (including micelles, bicelles, SUV and LUV) on fibril formation kinetics and fibril morphology has not yet systematically been analysed. Here we report that the interaction of IAPP with various membrane models promoted different processes of fibril formation. Our data reveal that in SDS and DPC micelles, IAPP adopts a stable α-helical structure for several days, suggesting that the micelle models may stabilize monomeric or small oligomeric species of IAPP. In contrast, zwitterionic DMPC/DHPC bicelles and DOPC SUV accelerate the fibril formation compared to zwitterionic DOPC LUV, indicating that the size of the membrane model and its curvature influence the fibrillation process. Negatively charged membranes decrease the lag-time of the fibril formation kinetics while phosphatidylethanolamine and cholesterol have an opposite effect, probably due to the modulation of the physical properties of the membrane and/or due to direct interactions with IAPP within the membrane core. Finally, our results show that the modulation of lipid composition influences not only the growth of fibrils at the membrane surface but also the interactions of β-sheet oligomers with membranes.