Aiming to address the requirements of Quadrotor Unmanned Aerial Vehicle (QUAV) for conducting mission cruises in three-dimensional complex environments, this paper introduces an optimization algorithm for trajectory planning. By analyzing the motion of the QUAV, the dynamics model is established, along with the constraint model for its flight trajectory. Based on the basic Particle Swarm Optimization (PSO) algorithm, simplified Particle Swarm Optimization (sPSO) removes the particle velocity term from the evolution equation. This adjustment helps prevent slower convergence and lower accuracy in the later stages, which can occur due to the dispersion of particles caused by the particle velocity term. The trajectory is smoothed by using the Minimum Snap principle to ensure that it meets the flight constraints of the QUAV. The simulation results demonstrate that the sPSO algorithm is effective and feasible for application in QUAV three-dimensional trajectory planning. In comparison to the PSO algorithm, the trajectory is more optimal, and the convergence accuracy is higher.