The nonlinear time-delay fast active queue management scalable transmission control protocol model was studied in this article. By analyzing the boundedness properties for solution trajectory of the fast active queue management scalable transmission control protocol model, the iterative relations of fast active queue management scalable transmission control protocol trajectory bounds were obtained. Furthermore, we calculated the maximum growth direction of the delay term in the integral interval and applied the backward method to calculate the lower conservative bound corresponding to each time of the delay term. Therefore, the global stability parameter condition of fast active queue management scalable transmission control protocol, which was less conservative than the existing global stability conditions, was obtained in this article. The validity of the stability conditions obtained in this article was verified by NS-2 simulation experiment.