AbstractIntegrin-mediated focal adhesions are the primary architectures that transmit forces between the extracellular matrix (ECM) and the actin cytoskeleton. Although focal adhesions are abundant on rigid and flat substrates that support high mechanical tensions, they are sparse in soft three-dimensional (3D) environments. Here we report curvature-dependent integrin-mediated adhesions called curved adhesions. Their formation is regulated by the membrane curvatures imposed by the topography of ECM protein fibres. Curved adhesions are mediated by integrin ɑvβ5 and are molecularly distinct from focal adhesions and clathrin lattices. The molecular mechanism involves a previously unknown interaction between integrin β5 and a curvature-sensing protein, FCHo2. We find that curved adhesions are prevalent in physiological conditions, and disruption of curved adhesions inhibits the migration of some cancer cell lines in 3D fibre matrices. These findings provide a mechanism for cell anchorage to natural protein fibres and suggest that curved adhesions may serve as a potential therapeutic target.