The establishment of a lunar base needs to solve the problem of energy supply first. Nuclear power system has the advantages of high power, long life and strong environmental adaptability, and is an ideal energy supply scheme for lunar base and other deep space exploration missions. Using low enriched uranium fuel is an important trend in the development of space nuclear power in recent years. In this paper, a core design of lunar base nuclear power system based on low enriched uranium molybdenum alloy fuel, heat pipe cooling system, Stirling thermoelectric conversion system and heat pipe radiator is proposed. The output power of the system is ≥ 40kWe, and its service life is 10 years. The core is designed by RMC program and CFD software, and the overall parameters of the core are given. The reactor core physics is analyzed and calculated. The results show that the system scheme is reasonable and feasible, and can meet the requirements within the service life.