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This work focuses on deriving the necessary and sufficient stability condition of transmission control protocol (TCP) network with a proportional-integral (PI) active queue management (AQM) scheme via a parameter space approach. First, a fluid-flow TCPs nonlinear model is converted into a linear time-delay system of neutral type. Second, the stability of the closed-loop system is characterized in terms of the networks and the controllers parameters. By simulation studies we investigate the boundarys relations of these two kinds of parameters in the parameter space and illustrate how PI controllers parameters affect the stability. Finally, different stability conditions are compared to show the less conservatism of our necessary- and sufficient-condition-based method, and simulation experiments by both Matlab and NS-2 are conducted to prove our claim.