We address the global asymptotic stability of FAST TCP, especially considering cross traffics, time-varying network feedback delay, and queuing delay dynamics at link. Exploiting the inherent dynamic property of FAST TCP, we construct two sequences that represent the lower and upper bound variations of the congestion window in time. By showing that the sequences converge to the equilibrium point of the congestion window, we establish that FAST TCP in itself is globally asymptotically stable without any specific conditions on the tuning parameter α or the update gain γ.