<p>Topology optimization offers a novel approach for the lightweight design of aerospace structures. A multi-objective topology optimization framework is proposed based on the level set method. The compromise programming approach is applied to the integration of objective functions to enhance the balance and stability of the optimization results. The final optimized structure has clear and smooth boundaries, which are conducive to model reconstruction and further optimization. Considering the stiffness and fundamental frequency of the structure, the configuration of the aircraft spoiler is optimized. A set of uniform Pareto frontier solutions is provided by changing the weights, and the material competition between different objectives is shown through the change of topological configuration. An optimization result in the Pareto frontier solution is employed as the example for model reconstruction and analysis. Compared with the traditional multi-spar and multi-rib structure, at the same mass level, the maximum displacement and von-Mises stress of the optimized structure are reduced by 34.55% and 41.49%, respectively, and the fundamental frequency is increased by 64.75%. The design framework can also be extended to multi-objective topology optimization design of other structures.</p>