Existing climbing robots achieve stable movements on limited surface types. However, adapting a single robot design to various surface shapes remains a substantial challenge. Based on the van der Waals (vdW) force-mediated adhesion mechanism of a gecko foot and negative pressure from octopus suckers, this study introduces a biomimetic integration strategy for designing and fabricating a pneumatically actuated switchable adhesion system (SAS). The SAS includes an adhesive material responsible for generating vdW forces and a suction cup with a membrane structure that enables a vacuum suction force. Owing to nonlinear superposition effects, this SAS exhibited a 56.4% higher adhesion force than the algebraic superposition of the vdW and vacuum suction forces. Moreover, the SAS offers a quick switch between adhesion and detachment through pneumatic modulation, achieving a synergistic balance between adaptability, robustness, and load-bearing efficiency. Equipped with this SAS, we developed a pneumo-electrically actuated quadruped-climbing robot that can climb planes with different tilt angles and surfaces with different curvatures.