We propose a novel design of a biomimetic micro-structured surface, which exhibits controlled strongly direction-dependent adhesion properties. The micro-system consists of parallel elastic wall-like structures covered by a thin layer. Numerical calculations have been carried out to study the adhesive properties of the proposed system and to provide design criteria with the aim of obtaining optimized geometries. A numerically equivalent version of the double cantilever beam fracture experiment is, then, simulated by means of finite element analysis to investigate the anisotropic adhesion of the structure. We find that, because of inherent crack trapping properties of these types of structures, the wall-like geometry allows us to strongly enhance adhesion when the detachment direction is perpendicular to the walls. On the other hand, when the detachment occurs parallel to the walls, the system shows low adhesion. This controlled direction-dependent adhesive property of the proposed structure solves one of the key problems of biomimetic adhesive surfaces, which usually show very strong adhesion, even larger than biological systems, but are not suitable for object manipulation and locomotion, as detachment always occurs at high loads and cannot be controlled.