Abstract: Orbits nearby the Earth-Moon libration points have the specific dynamic characteristicsand are the preferred position of relay satellites for the lunar farside exploration. For relay requirements of the future lunar farside exploration, the surface coverage of the Earth-Moon L2 periodic orbits is studied. Firstly, the continuation method calculating the halo orbit family is proposed with the circular restricted three-body problem. The south and north halo families with a large scope are calculated in the Earth-Moon system. Secondly, the coverage model of the lunar farside surface is presented for the relay satellites. The coverage factors are consequently defined. Finally, the coverage is numerically simulated. The results show that the coverage capacity is decided by the amplitude and style of L2 orbits. A halo orbit with small amplitude has an excellent entire coverage capacity, while a large one has a better coverage capacity for the south or north poles. Furthermore, the research can provide a beneficial reference for the orbit design of the future CHANG'E-4 mission.