Direct gas cooled closed Brayton cycle can efficiently convert the fission energy of the reactor into electricity, which is an ideal energy conversion system for space reactor. The pipe between the reactor outlet and turbine inlet is designated as the hot leg piping. To reduce effect of radiation heat dissipation on the cycle performance, the hot leg piping requires unique design features. In this paper, the mathematical models of the space Brayton cycle and the radiation heat dissipation of the hot leg piping are established, and the influence of the heat dissipation on the cycle performance is analyzed. The results show that the heat dissipation of hot leg piping decreases the cycle performance. The turbine inlet temperature decreases by 10K and the cycle efficiency decreases by 1.35%. Based on the numerical simulation method, insulation performance of hot leg piping is studied. The results show that the insulation performance of internal insulation is better than the external insulation. Internal insulation with low thermal conductivity and large thickness of insulation layer decrease the maximum temperature of the hot leg piping, reduce the radiation heat dissipation and improve the cycle performance. The higher the space environment temperature and the lower the emissivity of the coating material reduce the radiation heat dissipation. However, the maximum temperature is easy to exceed the limit of pipe material. The analysis provides a reference for the hot leg piping insulation design of the space closed Brayton cycle in the future.