A class of Internet network congestion control algorithms with communication delays is studied. By choosing the communication delay as a bifurcation parameter, the existence of Hopf bifurcation is proved. The formulas for determining the stability of bifurcation periodic solutions and the direction of the Hopf bifurcation are presented by applying the center manifold theorem and the normal form theory. The results have shown that the communication delay is one of the key factors to affect the quality of service (QoS) of Internet and plays an important role in communicating process of Internet. Finally, a numerical simulation is given to verify the theoretical results.