Plasma membranes in the human brain can interact with amyloid β-peptide (1-42; Aβ42) and induce Aβ42 fibrillation, which is considered to be a crucial process underlying the neurotoxicity of Aβ42 and the pathogenesis of Alzheimer's disease (AD). However, the mechanism of membrane-mediated Aβ42 fibrillation at the molecular level remains elusive. Here we study the role of adsorbed Aβ42 peptides on membrane-mediated fibrillation using supported lipid bilayers of varying phase structures (gel and fluid). Using total internal reflection fluorescence microscopy and interfacial specific second-order nonlinear optical spectroscopy, we show that the dynamics of 2D-mobile Aβ42 molecules, facilitated by the highly mobile lipids underneath the peptides, are critical to Aβ42 fibrillation on liquid phase membranes. This growth mechanism is retarded on gel phase membranes where the dynamics of 2D-mobile peptides are restricted by the "frozen" lipids with less mobility.