This paper developed a design and investigated the performance of 38 kWe turbo-machine unit for space nuclear reactor power systems with Closed Brayton Cycle (CBC) energy conversion. The compressor and turbine of this unit are scaled versions of the NASA's BRU developed in the sixties and seventies. The performance results of turbo-machine unit are calculated for rotational speed up to 45 krpm, variable reactor thermal power and system pressure, and fixed turbine and compressor inlet temperatures of 1144 K and 400 K. The analyses used a detailed turbo-machine model developed at the University of New Mexico that accounts for the various energy losses in the compressor and turbine and the effect of compressibility of the He-Xe (40 mole/g) working fluid with increased flow rate. The model also accounts for the changes in the physical and transport properties of the working fluid with temperature and pressure. Results show that a unit efficiency of 24.5% is achievable at rotation speed of 45 krpm and system pressure of 0.75 MPa, assuming shaft and electrical generator efficiencies of 86.7% and 90%. The corresponding net electric power output of the unit is 38.5 kWe, the flow rate of the working fluid is 1.667 kg/s, the pressure ratio and polytropic efficiency for the compressor are 1.60 and 83.1 %, and 1.51 and 88.3 % for the turbine.