Research on unmanned aerial vehicle (UAV) path planning technology in urban operation scenarios faces the challenge of multi-objective collaborative optimization. Currently, mainstream path planning algorithms, including the multi-objective particle swarm optimization (MOPSO) algorithm, generally suffer from premature convergence to local optima and insufficient stability. This paper proposes a Zaslavskii chaotic multi-objective particle swarm optimization (ZAMOPSO) algorithm to address these issues. First, three-dimensional urban environment models with asymmetric layouts, symmetric layouts, and no-fly zones were constructed, and a multi-objective model was established with path length, flight altitude variation, and safety margin as optimization objectives. Second, the Zaslavskii chaotic sequence perturbation mechanism is introduced to improve the algorithm’s global search capability, convergence speed, and solution diversity. Third, nonlinear decreasing inertia weights and asymmetric learning factors are employed to balance global and local search abilities, preventing the algorithm from being trapped in local optima. Additionally, a guidance particle selection strategy based on congestion distance is introduced to enhance the diversity of the solution set. Experimental results demonstrate that ZAMOPSO significantly outperforms other multi-objective optimization algorithms in terms of convergence, diversity, and stability, generating Pareto solution sets with broader coverage and more uniform distribution. Finally, ablation experiments verified the effectiveness of the proposed algorithmic mechanisms. This study provides a promising solution for urban UAV path planning problems, while also providing theoretical support for the application of swarm intelligence algorithms in complex environments.