Curvature is one of the most important features of lipid membranes in living cells, which significantly influences the structure of lipid membranes and their interaction with proteins. Taken the human islet amyloid polypeptide (hIAPP), an important protein related to the pathogenesis of type Ⅱ diabetes, as an example, we performed molecular dynamics (MD) simulations to study the interaction between the protein and the lipid structures with varied curvatures. We found that the lipids in the high curvature membrane pack loosely with high mobility. The hIAPP initially forms H-bonds with the membrane surface that anchored the protein, and then inserts into the membrane through the hydrophobic interactions between the residues and the hydrophobic tails of the lipids. hIAPP can insert into the membrane more deeply with a larger curvature and with a stronger binding strength. Our result provided important insights into the mechanism of the membrane curvature-dependent property of proteins with molecular details.