Abstract: There are several flight options for the Chang'E-2 spacecraft after its remaining at the Sun-Earth L2 point, for example, impacting the Moon or recapture into lunar orbit, returning to Earth orbit or atmospheric reentry, heading for halo orbits of the Earth-Moon L1 or L2 or the Sun-Earth L1 point, as well as flying by near-Earth asteroids in interplanetary space (Finally, Chang'E-2 successfully implemented a close flyby of Toutatis, a potentially hazardous near-Earth asteroid, on Dec.13, 2012). The analyses of these flight options require designing preliminary transfer trajectories with total velocity impulses no more than 100 m/s in four-body dynamics, in which the motion of the spacecraft is influenced by the gravities of the Sun, Earth, and Moon. In this study, we shall present low-energy Toutatis flyby trajectories from a Sun-Earth L2 quasi-periodic orbit, specifically, via a single lunar gravity assist that is intentionally utilized for exploring potential benefits, compared with the direct transfer manner that is adopted in the practical mission. Compared with the direct transfer trajectories to the asteroid, lunar gravity assist is demonstrated to be capable of saving propellant for the Toutatis flyby mission, and the equivalent velocity impulses are 58.46 m/s.