This study developed the conceptual core design of a 5kWth-class space heat pipe reactor that can be mounted on a launch vehicle and can be used on the lunar surface to continuously supply power in a space environment. It was designed to target the core of a nuclear reactor with a mass of less than 1200 kg, a height of less than 5 m, and a diameter of less than 2 m using low-enriched uranium fuel of less than 20 wt%. Studies were also carried out on reactor mass reduction and radiation shielding design for external devices.The design was developed for two types: a fast reactor using a U-7.5Mo fuel and a BeO reflector and an epi-thermal reactor using UO2 fuel rods, a ZrH1.5 moderator monolith/rods and a BeO reflector. Both types of reactors used high-assay low-enriched uranium (HALEU) with an enrichment of 19.5 wt% as fuel. By inserting the moderator rod inside the annular fuel, it was possible to achieve mass reduction of the reactor by softening the neutron spectrum and increasing the neutron utilization efficiency.