With the development of space technology and the in-depth study of the moon, it has become a future development trend to build a lunar base to achieve long-term sustainable exploration, resource development and utilization of the moon. As the basic guarantee for the operation of the lunar base, the power supply facility is the key. The long lunar night and extreme high and low temperature environment on the lunar surface put forward high requirements for the power supply. As an autonomous energy source, the nuclear reactor power has good environmental adaptability and can provide a continuous energy supply for the lunar base, which is an ideal choice for the energy facilities of the lunar base. This paper proposes a conceptual design scheme of a yttrium hydride moderated thermionic lunar reactor power supply core. The design life of the reactor is 7 years, and the net electric power is greater than 20 kilowatts. The reactor uses liquid metal sodium–potassium alloy as the coolant and relies on the control drum to adjust the reactivity. This paper introduces the structure and working principle of the core, and analyzes the neutronic characteristics of the core using the MCNP program. The power distribution of the reactor is given, the burnup of the reactor, the temperature effect of the materials are calculated, and the hydrogen leakage effect of the moderator is analyzed. This work can provide a certain reference for the selection and design of the lunar reactor power supply.