Internet represents a shared resource, wherein users contend for the finite network bandwidth. Contention among independent user demands can result in congestion, which, in turn, leads to long queuing delays, packet losses or both. Congestion control regulates the rate at which traffic sources inject packets into a network to ensure high bandwidth utilization while avoiding network congestion. In the current Internet, there are two mechanisms which deal with congestion, the end-to-end mechanism which is achieved by the Transmission Control Protocol (TCP) and the intermediate nodes algorithms such as Active Queue Management (AQM) in routers. In this thesis a combined model of TCP and AQM (TCP/AQM) is formulated and first simulated without controller. The results show that it is unable to track the desired queue size. So to get better tracking performance the Proportional Integral (PI) controller is used as AQM in the router queue, which shows good tracking performance, although the system response speed is slowed down. To speed up the system response and improve the performance of the PI controller, the Fuzzy Proportional Integral (FPI) controller is used as an active queue manager for congestion avoidance on Internet routers. Firstly the parameters of FPI controller are selected by trial and error method, but to get the best controller parameters the Genetic Algorithm (GA) is used as an off-line optimization method for tuning the FPI parameters, where using GA enhances overall system response. The results and analysis of the TCP/AQM system with FPI controller are verified and compared with those obtained with PI controller. The analytical results for linearized TCP/AQM model are presented in MATLAB version 7.0, while the verification of the designed controller for the TCP/AQM computer network is validated with packet-level simulations via Network simulator version 2.27. (NS2) package. From the obtained results, a faster response time as well as the regulation of the output to a constant value by the designed FPI controller is clearly observed and it is noted that the FPI controller provides good tracking performance under different circumstances for congestion avoidance in computer networks. .