A data migration system is provided for migrating data between an existing file server apparatus and a new file server apparatus in a computer system that includes a plurality of host computers and a plurality of file server apparatuses that are mutually connected to one another. The data migration system on the new file server apparatus copies file attributes unique to the network attached storage (NFS) and file attributes unique to the common internet file system (CIFS) from the existing file server apparatus, and stores the file attributes without changing the file attributes in the new file server apparatus. Then actual data is moved from the existing file server to the new file server. When a file access to data is made from a host computer during the file migration process, and if the data has not been migrated from the existing file server to the new file server, the data is read out from the existing file server onto the new file server, and the file access is processed by the new file server as if the existing file server were processing the file access.