To solve the problem that the parameter setting of the prescribed performance function depends on the initial tracking error value, a predefined time convergent sliding mode adaptive controller is designed for transmission control protocol (TCP) network systems with arbitrary initial state values, so that the real-time queue length tracking error of TCP network systems converges to zero within a predefined time and satisfies the prescribed performance function constraints. A tracking error conversion function is introduced to convert the queue lengthtrajectory tracking error with an arbitrary initial position into a new variable with an initial value at the origin, allowing the parameters of the prescribed performance function to be set arbitrarily in advance. A predefined time convergence sliding surface is designed, following, a predefined time convergent Lyapunov stability criterion is constructed, based on this stability criterion, the convergence time of close system can be set arbitrarily, and the upper bound of convergence time independent of the initial value and control parameters of the system. The hyperbolic tangent function approximates the control saturation constraint and converts the hyperbolic tangent function into a linear function with respect to the unconstrained control input variables; An adaptive Extreme Learning Machine(ELM) approximates the uncertain part of a TCP network system. Combining prescribed performance control and predefined time control methods, a sliding mode adaptive congestion controller with preset convergence time is designed. Numerical Simulation of TCP/AQM network congestion control with composite interference verifies the effectiveness and strong robustness of the algorithm.