We investigated the damage process of GFRP cross-ply laminates which have outer-ply 90° plies (e.g. [90/0]_s). While [0/90]_s laminates form symmetric cracks, staggered cracks occur in [90/0]_s laminates. To simulate the failure process of [90/0]_s laminates, we proposed a numerical model based on the finite element method. In this model, we used cohesive elements to simulate the occurrence and the propagation of ply cracks and delaminations. We found that simulated results agreed well with the experimental data. We confirmed the validity of the numerical model for the damage process of [90/0]_s laminates.