ART1 (adaptive resonance network) based neural network has been used for the purpose of discovering Web services of interest based on service classification. Non-functional properties of Web services can significantly improve the probability of having relevant output results. To achieve this task, we used the publicly available QWS Dataset as inputs for the neural network. The feature set is mainly dependent on several factors such as response time, throughput, availability, compliance, among others. Results show that there exists a relationship between possible non-functional properties in spit of non-uniform metrics. The use of neural networks provides a way to optimize the selection of the best available Web service. The average performance rate of the neural network is 92%. In all of the three trials conducted for testing this system, the neural network always converged into a solution which suggests that the use of neural networks in discovering the most suitable Web service can certainly be used. The proposed solution provides an effective discovery mechanism for finding the high quality Web services based on non-functional properties, however, there is room for improvement.