GridFTP has been used as a data transfer protocol to effectively transfer a large volume of data in Grid computing. GridFTP supports a feature called parallel data transfer that improves throughput by establishing multiple TCP connections in parallel. However, for achieving high GridFTP throughput, the number of TCP connections should be optimized based on the network status. In this paper, we propose an automatic parallelism tuning mechanism called GridFTP-APT (GridFTP with Automatic Parallelism Tuning) that adjusts the number of parallel TCP connections only using information measurable in the Grid middleware. Through simulation experiments, we demonstrate that GridFTP-APT significantly improves the performance of GridFTP in various network environments.