Low rate TCP DoS attack is a novel kind of attacks discovered by Kuzmanovic. According to several experiments, it is very effective in degrading the normal TCP sender?s throughput. FAST TCP is a delay-based transport layer protocol; it is used to transfer data in high bandwidth-delay environment. FAST TCP has a different congestion control mechanism from TCP Reno. Through simulations and test-bed experiments we demonstrate the Low rate TCP DoS attack to FAST TCP in high speed network. Analyses indicate that this kind of attack can affect the performance of FAST TCP. We also analyze the performance of the attack. At the end of this paper, two methods are proposed to mitigate the attack.