Abstract: A pair of superconducting insertion quadrupole magnets(SCQ), and a superconducting solenoid magnets(SSM) were used in the Beijing Electron-Positron Collider Upgrade（BEPCⅡ） in order to reduce the length of the beam, and to increase distinguish and identification ability of the particle. A cryogenic plant of 500 W at 4.5 K was to be built for the operation of the superconducting magnets. The paper described the cooling process for the SCQ and SSM magnets. Two kinds of cooling schemes for SCQ magnets, supercritical helium cooling and subcooled liquid helium cooling, were compared by numerical method. Thermal parameters of two kinds of cooling process were provided. Finally, the design of the subcooler, one of key components was presented.