China has implemented its change engineering. The first lunar satellite will be lunched in 2007. When it is on orbit and tracked and controlled by a ground-based TTC station, the zone of exclusion caused by the earth＇s rotation is about 50%. Although the coverage can be improved by scattered more earth stations along the longitude, the improvement effect is limited with the restriction of Chinese territory. Obviously, an on-orbit tracking and data relay satellite can enlarge the coverage. Based on the orbital elements, an algorithm to calculate the terms for a TDRS tracking a lunar satellite is presented here. Then the space coverage of a lunar satellite tracked by an earth station or a TDRS is computed. Their results show that compared with the tracking coverage of 32% or 50% made by an earth station, a TDRS can cover a lunar satellite by 61% with lunar exclusion or 90% without lunar exclusion. When a lunar satellite is tracked by a TDRS rather than an earth satellite, some extra requirements are added to the TDRS＇ antenna movement. These requirements are beyond the capability of the current on-orbit TDRS, which is designed for tracking low earth satellites. Finally, with the help of an earth station and a careful scheduler, a proposal is presented to further enlarge the tracking coverage for a current on-orbit TDRS tracking a lunar satellite.