Asteroid capture and mining is considered one of the most promising feasible solutions to the energy issue. However, the capture window is very brief. Therefore, time-optimized trajectory planning for the capturing device is crucial. This study considers a trajectory optimization problem for a flexible net system (FNS) to capture a designated asteroid target. The nonlinear dynamics and contact dynamics between the net and the asteroid are examined, simulating a task where using FNS with four actuators with three-axis thrusters to capture the asteroid Bennu. Then, a Particle Swarm Optimization (PSO) algorithm-enabled Generating Set Search (GSS) technique is proposed. This method models parameters of each polynomial trajectory as a particle, which automatically optimizes based on its own and the group’s experiences. The results show that trajectory optimization can improve capture average velocity by 147.0% to 261.4% compared to cases without trajectory optimization and without thrust. The results validate PSO-GSS trajectory optimization for rapid NEA capture.