The1 Lunar Hydrogen Mapper (LunaH-Map) will be one of 13 CubeSats to launch on the first integrated flight of NASA's Space Launch System and Orion spacecraft in 2018. The goal of the LunaH-Map mission is to map the hydrogen content of the entire South Pole of the moon, including permanently shadowed regions at high resolution. The spacecraft is a 6 U CubeSat and the main instrument is a neutron spectrometer which will be used to perform the measurements required to accomplish the primary science objective. Once LunaH-Map reaches the Moon, the spacecraft will perform a 60-day science mission, consisting of 141 science orbits during which the measurements will be taken. In the design of the LunaH-Map spacecraft, one of the main challenges is the telecommunication system as the spacecraft needs the ability to relay data during the long cruise phase and during the science phase. In addition, the telecommunication system needs to support the main navigation functions required to reach the Moon and to insert in the highly elliptical orbit required for the science phase. This paper covers the main aspects of the telecommunication design for the mission including: link and coverage analysis, waveform selection and spectral constraints, hardware selection and ground station coordination.