A learning method that uses neural networks for service quality control in the asynchronous transfer mode (ATM) communications network is described. Because the precise characteristics of the source traffic are not known and the service quality requirements change over time, building an efficient network controller which can control the network traffic is a difficult task. The proposed ATM network controller uses backpropagation neural networks for learning the relations between the offered traffic and service quality. The neural network is adaptive and easy to implement. A training data selection method called the leaky pattern table method is proposed to learn precise relations. The performance of the proposed controller is evaluated by simulation of basic call admission models.