For safe path planning of unmanned aerial vehicles (UAVs) in a three-dimensional (3D) environment with multiple threats, first, a cost function is introduced according to the terrain constraints and UAV overall performance constraints of the path planning problem. Then, improved nonlinear dynamic inertia weights (INDIW) are introduced into the particle swarm optimization (PSO) algorithm, and when the particles fall into the local optimum, the velocity is perturbed, and the velocity and improved nonlinear dynamic inertia weight PSO (VAINDIWPSO) algorithm are obtained. The algorithm improves the speed of convergence and fitness function value of the PSO algorithm. However, the impact of flyable path optimization is now not obvious. Therefore, to further enhance the overall performance of the VAINDIWPSO algorithm, the adaptive adjustment of the velocity is introduced, the chaotic initialization is carried out, and the improved logistic chaotic map is introduced into the algorithm, and an improved chaotic-VAINDIWPSO (IC-VAINDIWPSO) algorithm is obtained. Then, the corresponding relationship between the algorithm and constraints is used to efficiently search complicated environments and find paths with excessive security and small cost function. The simulation outcomes exhibit that in a complicated environment the IC-VAINDIWPSO algorithm substantially improves the speed of convergence of the algorithm, reduces the fitness function value of the algorithm and the initialization time of the algorithm, and the acquired path is additionally smoother. A near-optimal solution is obtained.