Mobile IP is a solution to support host mobility in the Internet. But, packets can be lost during the movement detection and registration periods of the Mobile IP. Regular TCP interprets theses packet losses as signs of network congestion, so it reduces its transmission rate by reducing its window size and slow start threshold. Besides, the multiple packet losses occurring during handoffs trigger successive retransmission timeouts at the TCP sender, causing a long communication pause even after handoff is completed. These together lead to significant throughput degradation. In this paper, we propose two new TCP schemes to reduce packet losses and to alleviate the effects of handoffs on TCP performance. TCP-MD (Movement Detection) is proposed to reduce packet losses by detecting a handoff earlier, and TCP-R (Registration) is designed to prevent packet losses by freezing data transmission during registration. The proposed schemes maintain end-to-end TCP semantics, making it possible to fully interoperate with the existing infrastructure. Only a small change is required in the mobile host, plus the implementation is simple because some Mobile IP messages are used to notify the handoff, eliminating the need for any additional messages. Simulations confirmed that the proposed schemes can give an excellent performance in an environment where the mobile host experiences frequent handoffs.