The use of lighter and high-performance materials in the aerospace sector is of great importance. Optimization methods, which have become very popular with the technological development in the production methods of composite structures in recent years and provide the most suitable design for the purpose, are frequently preferred in the design of parts in the aviation industry. Determining the buckling load capacity of a composite beam under compression load is very important for the design of composite structures. The buckling load capacity of a hybrid composite beam with fiber metal laminate (FML), which is frequently used between aircraft wing and fuselage. The optimum design of the anti-buckling behavior of the hybrid composite beam, which is subjected to compression load, fixed by simple support on both sides, was performed by a genetic algorithm (GA) based on the Tsai-Wu fracture criterion. The robust design of composite hybrid laminates was developed using a design optimization process based on GA with the finite element method. A multi-objective genetic algorithm (MOGA) was used to optimize the design of a hybrid composite beam subjected to buckling. Design variables in the optimization process are considered as fiber material and angle orientations. The purpose of the objective function is to reduce the equivalent stress of hybrid composites while increasing critical buckling load. The design constraint was the Tsai-Wu failure index. As a result, it has been observed that the buckling performance of the beam depends on the structure of the metal material in FML composites. Carbon/epoxy and glass/epoxy structures were proposed and a design was aimed according to the maximum buckling load in the best stacking sequence, taking into account the data in the design constraints.