The stability of the Newton-like algorithm in optimization flow control is considered in this paper.This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory, without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable, and all trajectories described by this algorithm ultimately converge to the equilibrium point.