The morphology and motion behavior of a cell are highly influenced by its external biological, chemical, and physical stimuli, and geometric confinement. In this paper, it is revealed that the mean curvature of the substrate significantly influences the adhesion of vesicles. By employing the variational method and investigating the Helfrich free energy, the configuration of axisymmetric vesicles adhered to curved spherical substrates is obtained theoretically. Moreover, numerical simulations based on the finite element method are also carried out to investigate the adhesion of vesicles on curved substrates with complex shapes. It is found that for a fixed area of a vesicle, its total free energy depends mainly on the mean curvature of the adhesion region but is insensitive to the specific shape of the substrate, and the total free energy monotonically decreases with the increase in the mean curvature. In addition, possible biological significances of the curvature-dependent adhesion, such as the shape of the cell and antibiofouling, are discussed. This study may deepen our understanding of the underlying mechanisms of adhesion in cellular activities.