Grid data management is a challenging task because of the heterogeneous, dynamic and large-scale nature of Grid environments. This paper proposes an autonomic Grid data management architecture based on virtualized distributed file systems and WSRF-compliant management services. Autonomic functions are integrated into the services to provide self-managing control over the different entities of Grid-wide file system sessions, in accordance with high-level objectives, and operate together to automatically achieve the desired data provisioning behaviors. Important autonomic features are designed and implemented in this system in the aspects of cache configuration, data replication and session redirection. Experiments with a prototype demonstrate that this architecture can automatically and substantially improve the performance and reliability of Grid data access.