The widespread application of composite structures in aerospace, biomedical, and other advanced fields imposes extremely high demands on their stability and reliability. However, due to their multi-scale characteristics, these structures often exhibit complex failure modes under complex loading conditions, involving the coupling of macroscopic global instability (such as buckling) and microscopic local instability (such as wrinkling). Traditional single-scale analysis methods often struggle to accurately capture both types of instability behaviors and their interaction mechanisms simultaneously. To overcome this limitation, this study developed a multi-scale framework based on computational homogenization theory, aiming to systematically reveal and quantify the cross-scale coupled failure mechanisms between global buckling and local wrinkling in composite structures. At the macro-scale, the updated Lagrangian formulation with Kirchhoff shell or Euler beam kinematics is employed to describe the large deformation of the structure, efficiently capturing its macro-scale buckling response. At the micro-scale, through-thickness representative volume elements (RVEs) are embedded at each integration point of the macroscopic model, and their inherent buckling modes are explicitly introduced as drivers for local instability. This approach naturally couples microscopic instability with the macroscopic mechanical field. The method explains how microstructural instability triggers and exacerbates macroscopic instability, and how macroscopic deformation fields influence the evolution of local wrinkling patterns. This framework offers value for the lightweight design, stability optimization, and failure prediction of composite structures.