Cryostat performance is essential for the stable operation of a superconducting magnet. A closed-cycle liquid helium cryostat was adopted for use for a superconducting electron cyclotron resonance (ECR) ion source by recondensing liquid helium vapor. The goal was to maintain the liquid helium filled reservoir at a constant level without transferring any liquid helium during the normal operation of the ECR ion source. To accomplish this, Gifford-McMahon (GM) refrigerators, which have two cold heads, were installed on the top of the cryostat. The cooling power of the GM cryocooler is 1.5 W at the second stage and 50 W at the first stage. Each stage was connected to the liquid helium reservoir, a radiation shield including high-Tc current lead, and related items. Before commissioning the ECR ion source, a preliminary evaluation of the recondensation performance was carried out with the magnet in partial operation. The design of the cryostat, its fabrication, and the experimental results are reported.