The trajectory planning of multiple unmanned aerial vehicles (UAVs) is the core of efficient UAV mission execution. Existing studies have mainly transformed this problem into a single-objective optimization problem using a single metric to evaluate multi-UAV trajectory planning methods. However, multi-UAV trajectory planning evolves into a many-objective optimization problem due to the complexity of the demand and the environment. Therefore, a multi-UAV cooperative trajectory planning model based on many-objective optimization is proposed to optimize trajectory distance, trajectory time, trajectory threat, and trajectory coordination distance costs of UAVs. The NSGA-III algorithm, which overcomes the problems of traditional trajectory planning, is used to solve the model. This paper also designs a segmented crossover strategy and introduces dynamic crossover probability in the crossover operator to improve the solving efficiency of the model and accelerate the convergence speed of the algorithm. Experimental results prove the effectiveness of the multi-UAV cooperative trajectory planning algorithm, thereby addressing different actual needs.