A decomposition strategy for the structural optimization of a fiber-reinforced aircraft wing box is proposed. The proposed method decomposes the wing-box optimization into two levels: a system-level and a subsystem-level optimization. The ribs are the subsystems of the problem. Each rib has a local set of design variables and constraints. The loads on the ribs are the crushing loads caused by the bending of the wing. At the system level, the wing-box skins are optimized while accounting for the effect of the skin design on the loads applied to the ribs. The sensitivity of the rib mass to the applied loads is evaluated using the Lagrange multipliers of the optimized rib design. To enhance the numerical efficiency of the two-level optimization, the changes of the loads on the ribs are subjected to a reduction by principal component analysis (PCA). In both the wing-level and rib-level optimization problems, the level-set strategy for the optimization of composite structures, previously introduced by the authors, is employed. This method permits an advantageous use of coarse and fine finite element models employing a standard commercial finite element code. The proposed method is applied to the design of a composite horizontal tail plane. The accuracy of and the computational time savings by the proposed PCA-based reduction scheme are quantified.