Hot Universe Baryon Surveyor (HUBS) is being conceptualized in China as a major X-ray mission for the next decade to look for "missing baryons". The superconducting transition-edge sensor is a key technology in HUBS, which needs to be worked at temperatures below 100 mK. In this paper, the HUBS cooling system will be designed and discussed. A 4 K mechanical cryocooler combined with adiabatic demagnetization refrigerator (ADR) will be employed in the preliminary design. Some test performance of two candidate models for precooling stage, the self-developed pulse tube cryocooler driven by linear compressor or thermal compressor, will be presented.