The emerging skin-integrated devices have been embedded with various functions, whose ideal implementation typically relies on intact bonding to curved substrates. However, the predeformation, which originates from the attachment of a thin film to a curved substrate, attempts to peel the film (i.e., self-debonding). It calls for strong enough interfacial adhesion in applications. On the other hand, too strong adhesion can destroy the surfaces of devices and substrates when the devices are peeled off after service. Therefore, seeking critical conditions becomes essential. Herein, we study the self-debonding of an adhesive thin film on a convex cylindrical surface. Taking Dugdale’s constant-stress law to describe the interfacial traction–separation relationship, we analytically unveil that the self-debonding behaviors are not solely determined by the interfacial energy. Instead, both the interfacial strength and critical interfacial separation are decisive. We thus obtain a phase diagram consisting of two critical conditions correspondingly. Similar results appear in the finite element analysis with the trapezoidal cohesive law, quantitatively showing the evolution of deflection and interfacial detachment force. Furthermore, we find that the circular film, symmetrically adhering to a spherical surface with small deflection, can still share similar self-debonding behavior. Our results provide guidance on how to stick a thin film on a convex cylindrical or spherical surface well with proper interfacial adhesion.