The biogenesis and maintenance of thylakoid membranes require vesicle-inducing protein in plastids 1 (VIPP1). VIPP1 is a member of the endosomal sorting complex required for transport-III (ESCRT-III) superfamily, whose members form diverse filament-based supramolecular structures that facilitate membrane deformation and fission. VIPP1 cryo-electron microscopy (EM) structures in solution revealed helical rods and baskets of stacked rings, with amphipathic membrane-binding domains in the lumen. However, how VIPP1 interacts with membranes remains largely unknown. Here, using high-speed atomic force microscopy (HS-AFM), we show that VIPP1 assembles into right-handed chiral spirals and regular polygons on supported lipid bilayers via ESCRT-III-like filament assembly and dynamics. VIPP1 filaments grow clockwise into spirals through polymerization at a ring-shaped central polymerization hub, and into polygons through clockwise polymerization at the sector peripheries. Interestingly, VIPP1 initially forms Archimedean spirals, which upon maturation transform into logarithmic spirals through lateral annealing of strands to the outermore low-curvature spiral turns.