The fiber-reinforced composite stringer is commonly used in large civil aircraft wing structures. Under compression loads, it exhibits complex failure modes, with matrix cracking being one of the most common. The quantitative analysis of matrix failure is important and difficult. To address this issue, a multiscale method combining the generalized method of cells (GMC) and macroscopic FEM models is employed to quantitatively predict matrix damage and failure. The extent of matrix damage in the composite structure is represented by the number of failed matrix subcells within the repeating unit cells. The 3D Tsai–Hill failure criterion is established for the matrix phase, and the maximum stress failure criterion is applied to the fiber subcell. Upon meeting the criterion, the stiffnesses of the failed subcells are immediately reduced to a nominal value. In the current study, the ultimate loads, failure modes and load–displacement curves of composite stringers subjected to compressive load are obtained by the experiment approach and the proposed multiscale model. The experimental and simulation results show good agreement, and the multiscale analysis method successfully predicts the extent of matrix damage in the composite stringer under compressive load. The number of failed matrix subcells quantitatively evaluates the damage extent within a 2 × 2 GMC model. The findings reveal that matrix subcell failures primarily occur in the 45° and −45° plies of the middle part of the stringer composite.