ESCRT-III is required for lipid membrane remodeling in many cellular processes, from abscission to viral budding and multi-vesicular body biogenesis. However, how ESCRT-III polymerization generates membrane curvature remains debated. Here, we show that Snf7, the main component of ESCRT-III, polymerizes into spirals at the surface of lipid bilayers. When covering the entire membrane surface, these spirals stopped growing when densely packed: they had a polygonal shape, suggesting that lateral compression could deform them. We reasoned that Snf7 spirals could function as spiral springs. By measuring the polymerization energy and the rigidity of Snf7 filaments, we showed that they were deformed while growing in a confined area. Furthermore, we observed that the elastic expansion of compressed Snf7 spirals generated an area difference between the two sides of the membrane and thus curvature. This spring-like activity underlies the driving force by which ESCRT-III could mediate membrane deformation and fission.