TCP Redirection (TCP-R) is an extension of TCP, which maintains active TCP connections when the disconnection occurs due to IP address changes. In mobile computing environments, IP addresses may be changed frequently as the host moves across subnets or changes network devices. However, it is difficult for most stateful network applications to work continuously in that situation. There is much research to support such dynamics in the network layer, but these attempts in the IP layer tend to incur some complexity. This paper intends to investigate the end-to-end mobility support in the transport layer. We developed a simple redirection mechanism for TCP, which enables us to keep our working activities continuous without any intermediate agents for IP packet forwarding. We also show that TCP-R enables the intentional replacement of IP addresses, which is useful for certain network services. We implemented and evaluated a prototype of TCP-R. The measured performance indicates that TCP-R can realize continuous operation with minimal overhead and complexity.