As the second of Earth's Trojan asteroids, 2020 XL5 is worthy of rendezvous and even sample return missions in many aspects. In this paper, a rendezvous mission to Earth's second Trojan asteroid 2020 XL5 is proposed. However, due to its high inclination and large eccentricity, direct impulsive transfer requires large amounts of fuel consumption. To address this challenge, we explore the benefits of electric propulsion and multi-gravity assist techniques for interplanetary missions. These two techniques are integrated in this mission design. The design of a low-thrust gravity-assist (LTGA) trajectory in multi-body dynamics is thoroughly investigated, which is a complex process. A comprehensive framework including three steps is presented here for optimization of LTGA trajectories in multi-body dynamics. The rendezvous mission to 2020 XL5 is designed with this three-step approach. The most effective transfer sequence among the outcomes involves Earth–Venus–Earth–Venus-2020 XL5. Numerical results indicate that the combination of electric propulsion and multi-gravity assists can greatly reduce the fuel consumption, with fuel consumption of 9.03%, making it a highly favorable choice for this rendezvous mission.