A spacecraft placed in an Earth-Moon L2 quasi-halo orbit can maintain constant communication between the Earth and the far side of the Moon. This quasi-halo orbit could be used to establish a lunar space station and serve as a gateway to explore the solar system. For a mission in an Earth-Moon L2 quasi-halo orbit, a spacecraft would have to be transferred from the Earth to the vicinity of the Earth-Moon L2 point, then inserted into the Earth-Moon L2 quasi-halo orbit. Unlike the near Earth case, this orbit is essentially very unstable due to mutually perturbing gravitational attractions by the Earth, the Moon and the Sun. In this paper, an insertion maneuver of a spacecraft into an Earth-Moon L2 quasi-halo orbit was investigated using the global optimization algorithm, including simulated annealing, genetic algorithm and pattern search method with collision avoidance taken into consideration. The result shows that the spacecraft can maintain its own position in the Earth-Moon L2 quasi-halo orbit and avoid collisions with threatening objects.