Feed Forward Artificial Neural Networks are the most widely used models to explain the information processing mechanism of the brain. Network topology plays a key role in the performance of the feed forward neural networks. Recently, the small-world network topology has been shown to meet the properties of the real life networks. Therefore, in this study, we consider a feed forward artificial neural network with small-world topology and analyze its performance on classifying the epilepsy. In order to obtain the small-world network, we follow the Watts-Strogatz approach. An EEG dataset taken from healthy and epileptic patients is used to test the performance of the network. We also consider different numbers of neurons in each layer of the network. By comparing the performance of small-world and regular feed forward artificial neural networks, it is shown that the Watts-Strogatz small-world network topology improves the learning performance and decreases the training time. To our knowledge, this is the first attempt to use small-world topology in a feed forward artificial neural network to classify the epileptic case.