We propose a wavelet neural network (WNN) control method for active queue management (AQM) in an end-to-end TCP network, which is trained by adaptive learning rates (ALRs). In the TCP network, AQM is important to regulate the queue length by passing or dropping the packets at the intermediate routers. RED, PI, and PID algorithms have been used for AQM. But these algorithms show weaknesses in the detection and control of congestion under dynamically changing network situations. In our method, the WNN controller using ALRs is designed to overcome these problems. It adaptively controls the dropping probability of the packets and is trained by gradient-descent algorithm. We apply Lyapunov theorem to verify the stability of the WNN controller using ALRs. Simulations are carried out to demonstrate the effectiveness of the proposed method.