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Analysis and control of nonlinear dynamical models of Internet congestion control system has been an interested issue in recent years. In this paper the bifurcation behavior of the TCP-like model of Internet congestion control system including TCP and AQM is investigated. In particular, the effects of system parameters on nonlinear dynamical behavior and the condition for period-doubling bifurcation and chaos occurrence will be revealed. After that an adaptive controller will be proposed for controlling chaos in this system. This controller is based on model reference adaptive system (MRAS) method for a linearized system with delay. Simulation results demonstrate that the complex behavior of the system can be controlled by our method.