A large-scale cryopumping system using low-temperatute (3.5 K) liquid helium (LHe) was installed in an axisymmetrized tandem mirror GAMMA 10 at the Plasma Research Center, University of Tsukuba, in order to obtain a clean vacuum condition with a larger pumping speed. This paper describes the detailed design of the system and the estimation of the improvement of the vacuum state and of the effectiveness on the plasma confinement. Four cryopumps are located in the end-mirror tanks and in the NBI tanks of the anchor regions on both sides. Performance tests of the cryopump with a set of simple pressure-balance equations have confirmed that the measured pumping speed agrees well with the designed value. Use of this pumping system has made it possible to reduce the base pressure in the plug/barrier to below 1×10^-6 Pa and upgraded thermal-barrier experiments were succesfully carried out under the improved vacuum condition.