Mobile IP network provides hosts the connectivity to the Internet while changing locations. However, when using TCP Vegas over a mobile network, it may respond to a handoff by invoking a congestion control algorithm, thereby resulting in performance degradation, because TCP Vegas is sensitive to the change of RTT (Round-Trip Time) and it may recognize the increased RTT as a result of network congestion. Since TCP Vegas could not differentiate whether the increased RTT is due to route change or network congestion. This work investigates how to improve the performance of Vegas after a Mobile IP handoff and proposes a variation of TCP Vegas, so-called Demo-Vegas, which is able to detect the movement of two end-hosts of a connection, and re-measure the BaseRTT (Minimum Round-Trip Time) if necessary. The proposed mechanism maintains end-to-end semantics, and operates under the existing network infrastructure. Demo-Vegas presents a simple modification in the two end sides of a connection and uses one reserved bit in TCP header. Simulation results demonstrate that Demo-Vegas features higher performance than Vegas in Mobile IP networks.