A handoff apparatus and method in FMIPv6 for seamless TCP packet transmissions. The handoff method includes steps of intercepting by a previous access router certain TCP packets sent from a correspondent node to a previous temporary address of a mobile node; and creating a TCP ACK by the previous access router in response to the certain TCP packets and sending by the previous access router the created TCP ACK to the correspondent node every time the certain TCP packets are forwarded to a new access router through a bi-directional tunnel. The handoff method has an advantage in that the packet transmission rate can be secured at the same level as the mobile node stays still during the performance of the handoff of the mobile node since the previous access router instead of the mobile node creates and sends the TCP ACK to the correspondent node during the performance of the handoff of the mobile node.