Gecko-inspired van der Waals force-based adhesion technology demonstrates significant potential for robotic operations. While superior adhesion is achieved under parallel contact during testing, engineering operations often involve non-parallel contact, weakening adhesion, and compromising task stability and efficiency. Stable attachment under such non-parallel contacts remains challenging. Inspired by the soft muscle and rigid bone in the gecko’s sole, this study proposes a self-adaptive core-shell dry adhesive by embedding a thin, rigid piece into a soft, thick elastomer comprising a top adhesion tip with a mushroom-like geometry for interfacial adhesion based on the van der Waals force and a bottom core-shell configuration for interface stress regulation. Unlike traditional core-shell structures with a fixed “dead core,” the proposed “live core” rotates within the soft shell, mimicking skeletal joints. This enables stress equalization at the interface and facilitates adaptive contact to macroscopic interfacial angle errors. This innovative core-shell configuration demonstrates an adhesion strength 100 times higher than conventional homogeneous structures under non-parallel contact and offers anti-overturning ability by mitigating torsional effects. The proposed strategy can advance the development of gecko-inspired adhesion-based devices and systems.