Abstract During terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme.