Enhanced adhesion on rough surfaces is highly desired for a wide range of applications. On the other hand, surface roughness compatibility and structure stability are two critical but competing factors for biologically-inspired dry adhesives in the real world. Inspired by ladybug, a hierarchical structural composite dry adhesive (denoted as PP-M) with enhanced robustness on surface roughness is developed, which is composed of a thin compliant contact layer (a thin soft PDMS film supported discretely by PDMS micropillars) and a rigid bottom layer (MREs). The PP-M shows a high pull-off strength of 8.2 N/cm2 on a smooth surface and nano-scale rough surface at a mild preload (2 N/cm2). For micro-scale rough surfaces, the PP-M exhibits better surface adaptability compared to the double-layered adhesive (PDMS on MRE) without micropillar support. The increased compliance of the contact layer also leads to a 2.11-fold superior pull-off strength at a wider range of roughness (Sq> 2.23μm). Element Analysis confirms PP-M's enhanced adaptability, attributed to deeper indentation and lower contact stress. This hierarchical composite structure in PP-M, characterized by a "soft on top and hard on bottom" stiffness distribution, synergizes the flexible contact layer with the stiff MRE bottom layer, leading to superior bonding properties. The results provide a new reference for achieving enhanced adhesion on rough surfaces.